Thermodynamics
MCQs
System and Surrounding
The part of universe which is under study is called system and the rest part of the universe is called surrounding. That means the universe is the combination of system and surrounding.
The part of universe which is under study is called system and the rest part of the universe is called surrounding. That means the universe is the combination of system and surrounding.
Types of System
Open System
The system which can exchange both heat and matter with the surrounding is called open system. Hot water in a beaker is an example of this system.
Closed System
The system which can exchange only heat but not matter with the surrounding is called closed system. Hot water in a sealed tube is an example of this system.
Isolated System
The system which can exchange neither energy nor matter with the surrounding is called Isolated system. Hot water in a thermos flask is an example of this system.
Open System
The system which can exchange both heat and matter with the surrounding is called open system. Hot water in a beaker is an example of this system.
Closed System
The system which can exchange only heat but not matter with the surrounding is called closed system. Hot water in a sealed tube is an example of this system.
Isolated System
The system which can exchange neither energy nor matter with the surrounding is called Isolated system. Hot water in a thermos flask is an example of this system.
Thermodynamic Process
When a system changes itself from one to another state, the operation is called procss.
Isothermal Process
The process which takes place at constant temperature is called isothermal process.
i.e. ΔT=O
Adiabatic Process
The process in which no heat change occurs is called adiabatic process.
i.e. ΔQ=O
Isochoric Process
The process which takes place at constant volume is called isochoric process.
i.e. ΔV=O
Isobaric Process
The process which takes place at constant pressure is called isobaric process.
i.e. ΔP=O
Cyclic Process
When a system undergoes a number of different processes and finally returns to its initial state, it is termed as cyclic process.
In cyclic process change in all state function will be zero. i.e. ΔE = 0, ΔH = 0, ΔP = 0, ΔT = 0
Reversible Process
The process which takes place infinitesimally slowly and whose direction at any point can be reversed by applying an infinitesimal change in the state of the system is called reversible Process. It is an ideal process. Work obtained in expansion is maximum and system is in virtual equilibrium at any state.
Irreversible Process
The process which takes place in one step and can not be reversed. This is a fast process. All natural processes are irreversible and system is in equilibrium only at initial and final state.
Spontaneous Process and Nonspontaneous Process
The process which proceeds of its own accord without any outside assistance or help is called Spontaneous Process or Natural Process and the reverse process which does not proceed on its own accord is called nonspontaneous process.
Spontaneous process is unidirectional, for reverse change work has to be done. For spontaneous process time is no factor. It may takes palce rapidly or very slowly. If a system is not in equilibrium state, a spontaneous change is inevitable. The change will continue untill equilibrium exist. Once the system attains the equilibrium it does not undergo further spontaneous change. Spontaneous process or change is accompanied by decrease of internal energy of enthalpy.
The tendency of a process to occur naturally is called Spontaniety.
Examples
A rolling ball down the hill spontaneously but it will not rall uphill unless work is done on it.
When two metal ball one hot and one cold are connected to each other, the heat flow from hotter to colder ball spontaneously but can never from colder to hotter ball spontaneously.
When a system changes itself from one to another state, the operation is called procss.
Isothermal Process
The process which takes place at constant temperature is called isothermal process.
i.e. ΔT=O
Adiabatic Process
The process in which no heat change occurs is called adiabatic process.
i.e. ΔQ=O
Isochoric Process
The process which takes place at constant volume is called isochoric process.
i.e. ΔV=O
Isobaric Process
The process which takes place at constant pressure is called isobaric process.
i.e. ΔP=O
Cyclic Process
When a system undergoes a number of different processes and finally returns to its initial state, it is termed as cyclic process.
In cyclic process change in all state function will be zero. i.e. ΔE = 0, ΔH = 0, ΔP = 0, ΔT = 0
Reversible Process
The process which takes place infinitesimally slowly and whose direction at any point can be reversed by applying an infinitesimal change in the state of the system is called reversible Process. It is an ideal process. Work obtained in expansion is maximum and system is in virtual equilibrium at any state.
Irreversible Process
The process which takes place in one step and can not be reversed. This is a fast process. All natural processes are irreversible and system is in equilibrium only at initial and final state.
Spontaneous Process and Nonspontaneous Process
The process which proceeds of its own accord without any outside assistance or help is called Spontaneous Process or Natural Process and the reverse process which does not proceed on its own accord is called nonspontaneous process.
Spontaneous process is unidirectional, for reverse change work has to be done. For spontaneous process time is no factor. It may takes palce rapidly or very slowly. If a system is not in equilibrium state, a spontaneous change is inevitable. The change will continue untill equilibrium exist. Once the system attains the equilibrium it does not undergo further spontaneous change. Spontaneous process or change is accompanied by decrease of internal energy of enthalpy.
The tendency of a process to occur naturally is called Spontaniety.
Examples
A rolling ball down the hill spontaneously but it will not rall uphill unless work is done on it.
When two metal ball one hot and one cold are connected to each other, the heat flow from hotter to colder ball spontaneously but can never from colder to hotter ball spontaneously.
Extensive and Intensive Properties
Properties which depend upon the amount of the substance present in the system are called extensive properties. Mass, Volume, Number of moles, Enthalpy, Entropy, Free energy, Heat Capacity, Force, Surface Area etc are the example of extensive properties. These properties are additive. If mass of the gas is changed, the volume is also changed and so is the number of moles and their internal energy of the system.
Properties which don't depend upon the amount of the substance present in the system are called intensive properties. Temperature, Pressure, Boiling Point, Melting Point, Specific Heat, pH, Vapour Pressure, Surface Tension, Viscosity etc are the example of intensive properties. If temperature of a glass of water is 25oC, then each and every drop of water in this glass has the temperatue of 25oC. These properties are non additive.
Properties which depend upon the amount of the substance present in the system are called extensive properties. Mass, Volume, Number of moles, Enthalpy, Entropy, Free energy, Heat Capacity, Force, Surface Area etc are the example of extensive properties. These properties are additive. If mass of the gas is changed, the volume is also changed and so is the number of moles and their internal energy of the system.
Properties which don't depend upon the amount of the substance present in the system are called intensive properties. Temperature, Pressure, Boiling Point, Melting Point, Specific Heat, pH, Vapour Pressure, Surface Tension, Viscosity etc are the example of intensive properties. If temperature of a glass of water is 25oC, then each and every drop of water in this glass has the temperatue of 25oC. These properties are non additive.
Internal Energy (E or U)
All forms of energy associated with a system is called internal energy or simply energy of the system (E).
This is expressed in Joule. This arises due to movement of molecules, arrangement of atoms in molecules, number of arrangement of electrons in atoms etc.
It is neither possible nor necessary to calculate the absolute value of internal energy of a system. It is a state function so depend only on the initial and final state of the system.
ΔE = Ef – Ei
In a reaction- R → P
ΔE = EP – ER
If Ef > Ei, ΔE is + ve
if Ef < Ei, ΔE is – ve
All forms of energy associated with a system is called internal energy or simply energy of the system (E).
This is expressed in Joule. This arises due to movement of molecules, arrangement of atoms in molecules, number of arrangement of electrons in atoms etc.
It is neither possible nor necessary to calculate the absolute value of internal energy of a system. It is a state function so depend only on the initial and final state of the system.
ΔE = Ef – Ei
In a reaction- R → P
ΔE = EP – ER
If Ef > Ei, ΔE is + ve
if Ef < Ei, ΔE is – ve
Sign Conventions for Work and Heat
W is +ve when work is done on the system W is – ve when work is done by the system q is +ve when the heat is being absorbed by the system q is – ve when the heat is evolved by system
W is +ve when work is done on the system W is – ve when work is done by the system q is +ve when the heat is being absorbed by the system q is – ve when the heat is evolved by system
Heat Capacity
The amount of heat required to change its temperature by one degree of a substance.
Q = CΔT
or, C = Q/ΔT
The amount of heat required to change its temperature by one degree of a substance.
Q = CΔT
or, C = Q/ΔT
Molar Heat Capacity
The amount of heat required to change its temperature by one degree of one mole of a substance.
The amount of heat required to change its temperature by one degree of one mole of a substance.
Heat Capacity at Constant Pressure (Cp)
The amount of heat required to change its temperature by one degree of a substance at constant pressure.
The amount of heat required to change its temperature by one degree of a substance at constant pressure.
Heat Capacity at Constant Volume (Cv)
The amount of heat required to change its temperature by one degree of a substance at constant volume.
The amount of heat required to change its temperature by one degree of a substance at constant volume.
Relation between CP and CV
We know that
H = E + PV
or, H = E + RT (as PV = RT for one mole)
differentiating the above equation w.r.t T, we get-
dH/dT = dE/dT + R(dT/dT)
or, CP = CV + R
or, CP − CV = R
We know that
H = E + PV
or, H = E + RT (as PV = RT for one mole)
differentiating the above equation w.r.t T, we get-
dH/dT = dE/dT + R(dT/dT)
or, CP = CV + R
or, CP − CV = R
First law of Thermodynamics
It is also called energy conservation principle. According to this principle, energy can neither be created nor be destroyed, it can only be transfer or change fron one form to another form.
In other way-
Heat absorbed (Q) by the system is equal to change in internal energy (ΔE) plus work done by the system (−W).
Q = ΔE + (−W)
or, ΔE = Q + W
During an isothermal process, the temperature of the system remains constant and hence ΔE = 0
so, 1st law of thermodynamics becomes-
Q = −W
or, −Q = W
Therefore, in isothermal process-
Heat absorbed by the system is equal to work done by the system or Heat evolved by the system is equal to work done on the system.
During adiabatic process, the system acts an isolated system and hence q = 0 so, 1st law of thermodynamics becomes-
ΔE = W
Therefore, Work done on the system is equal to increase in internal energy of the system i.e., when a gas is compressed adiabatically its internal energy increases or Work done by the system is equal to decrease in internal energy of the system, i.e., when a gas is expanded adiabatically its internal energy decreases.
During Cyclic Process, ΔE = 0
Q = −W
Therefore, in cyclic process, work done by the system is equal to heat absorbed by the system or work done on the system is equal to heat evolved by the system.
Limitations
First law does not indicate whether heat can flow from a cold body to a hot body or not.
First law does not specify that process is feasible or not.
Practically it is not possible to convert the heat energy into an equivalent amount of work.
It is also called energy conservation principle. According to this principle, energy can neither be created nor be destroyed, it can only be transfer or change fron one form to another form.
In other way-
Heat absorbed (Q) by the system is equal to change in internal energy (ΔE) plus work done by the system (−W).
Q = ΔE + (−W)
or, ΔE = Q + W
During an isothermal process, the temperature of the system remains constant and hence ΔE = 0
so, 1st law of thermodynamics becomes-
Q = −W
or, −Q = W
Therefore, in isothermal process-
Heat absorbed by the system is equal to work done by the system or Heat evolved by the system is equal to work done on the system.
During adiabatic process, the system acts an isolated system and hence q = 0 so, 1st law of thermodynamics becomes-
ΔE = W
Therefore, Work done on the system is equal to increase in internal energy of the system i.e., when a gas is compressed adiabatically its internal energy increases or Work done by the system is equal to decrease in internal energy of the system, i.e., when a gas is expanded adiabatically its internal energy decreases.
During Cyclic Process, ΔE = 0
Q = −W
Therefore, in cyclic process, work done by the system is equal to heat absorbed by the system or work done on the system is equal to heat evolved by the system.
Limitations
First law does not indicate whether heat can flow from a cold body to a hot body or not.
First law does not specify that process is feasible or not.
Practically it is not possible to convert the heat energy into an equivalent amount of work.
Work done in Isothermal and Reversible Expansion
Let us consider 'n' moles of an ideal gas enclosed in a cylinder fitted with a frictionless, weightless and movable piston. Let P be the pressure of the gas and P-dP be the external pressure under which volume of the gas increased by dV, then work done in this expansion is
dw = −(P − dP)dV = − PdV (as dP.dV is very small).
For a infinite volume change from V1 to V2, the total work done during expansion-
where P1 and P2 are the initial and final pressure respectively.
Question: 3 moles mole of and ideal gas are expanded isothermally and reversibly from volume of 10 m3 to the volume 20 m3 at 300 K. Claculate the work done by the system. (Answer: 5.178 KJ)
Let us consider 'n' moles of an ideal gas enclosed in a cylinder fitted with a frictionless, weightless and movable piston. Let P be the pressure of the gas and P-dP be the external pressure under which volume of the gas increased by dV, then work done in this expansion is
dw = −(P − dP)dV = − PdV (as dP.dV is very small).
For a infinite volume change from V1 to V2, the total work done during expansion-
where P1 and P2 are the initial and final pressure respectively.
Question: 3 moles mole of and ideal gas are expanded isothermally and reversibly from volume of 10 m3 to the volume 20 m3 at 300 K. Claculate the work done by the system. (Answer: 5.178 KJ)
Entropy (S)
It is a thermodynamic state function that is a measure of the randomness and disorderness of the molecules of the system. Greater the randomness, greater would be entropy. It is denoted by 'S'. As it is a state function so depends upon initial and final satate only. So change in entropy
ΔS = Sfinal − Sinitial
For a reversible process at constant temperature,the change in entropy is equal to energy absorbed or evolved divided by the temperature.
ΔS = q/T
If heat is absorbed, ΔS is positive and entropy increases while If heat is evolved, ΔS is negative and entropy decreases.
If heat change takes place at different temperatures, then-
dS = dq1/T1 + dq2/T2 + dq3/T3 + ... = Σ(dqrev/dT)
or, ∫ds = ∫dqrev/T
ΔS = ΔS + ΔS
at equilibrium, ΔS = 0
Unit
Cal K-1
or, J K-1
It is a thermodynamic state function that is a measure of the randomness and disorderness of the molecules of the system. Greater the randomness, greater would be entropy. It is denoted by 'S'. As it is a state function so depends upon initial and final satate only. So change in entropy
ΔS = Sfinal − Sinitial
For a reversible process at constant temperature,the change in entropy is equal to energy absorbed or evolved divided by the temperature.
ΔS = q/T
If heat is absorbed, ΔS is positive and entropy increases while If heat is evolved, ΔS is negative and entropy decreases.
If heat change takes place at different temperatures, then-
dS = dq1/T1 + dq2/T2 + dq3/T3 + ... = Σ(dqrev/dT)
or, ∫ds = ∫dqrev/T
ΔS = ΔS
at equilibrium, ΔS = 0
→→→→→→→
→→→→→→→
→→→→→→→
→→→→→→→
well orderd
Low Entropy
→→→→→→→
→→→→→→→
→→→→→→→
well orderd
Low Entropy
→↑←↓→←↓→
→←↓→↑←↓→
→↓←↓→↑←↓
←↑→↓←↓→↑
Random
High Entropy
→←↓→↑←↓→
→↓←↓→↑←↓
←↑→↓←↓→↑
Random
High Entropy
Cal K-1
or, J K-1
Gibbs free energy(G or F)
Gibbs free energy is the property of the system whose decrease is the measure of the maximum external work available during the transformation of system reversibly at constant pressure and temperature and it is a state function. So depend only on initial and final state of the system.
If S is the entropy of a system at ToK and H is its enthalpy then, Gibbs free energy is mathematically expressed as-
G = H - TS
On differentiation we get,
ΔG = ΔH − TΔS − SΔT
we know that- ΔH = ΔE + PΔV + VΔP
so, ΔG = ΔE + PΔV + VΔP − TΔS − SΔT
or, ΔG = ΔA + PΔV + VΔP − SΔT (as ΔE − TΔS = ΔA (work function))
at constant pressure and temperature-
or, ΔG = ΔA + PΔV
or, ΔG = −Wmax + PΔV (as W = −ΔA from 1st law of thermodynamics)
or, −ΔG = Wmax − PΔV
PΔV is the work done due to expansion against a constant pressure. So, decrease in free energy accompanying a process which occurs at constant pressure and temperature is the maximum work obtained from the system other than PΔV. Hence it is also called Net Work.
So, Net Work = −ΔG
Gibbs free energy is the property of the system whose decrease is the measure of the maximum external work available during the transformation of system reversibly at constant pressure and temperature and it is a state function. So depend only on initial and final state of the system.
If S is the entropy of a system at ToK and H is its enthalpy then, Gibbs free energy is mathematically expressed as-
G = H - TS
On differentiation we get,
ΔG = ΔH − TΔS − SΔT
we know that- ΔH = ΔE + PΔV + VΔP
so, ΔG = ΔE + PΔV + VΔP − TΔS − SΔT
or, ΔG = ΔA + PΔV + VΔP − SΔT (as ΔE − TΔS = ΔA (work function))
at constant pressure and temperature-
or, ΔG = ΔA + PΔV
or, ΔG = −Wmax + PΔV (as W = −ΔA from 1st law of thermodynamics)
or, −ΔG = Wmax − PΔV
PΔV is the work done due to expansion against a constant pressure. So, decrease in free energy accompanying a process which occurs at constant pressure and temperature is the maximum work obtained from the system other than PΔV. Hence it is also called Net Work.
So, Net Work = −ΔG
Variation of Free Energy with Temperature and Pressure
We know that-
F = H − TS -----(equation-1)
or, F = E + PV − TS (as H = E + PV)
differentiating this equation we get-
dF = dE + PdV + VdP − TdS − SdT
or, dF = dq + VdP − TdS − SdT (as dq = dE + PdV)
or, dF = TdS + VdP − TdS − SdT (as dqrev/T = dS)
or, dF = VdP − SdT -----(equation-2)
at constant Temperature-
or, dF = VdP
or, (dF/dP)T = V -----(equation-3)
and at constant Pressure-
or, dF = − SdT
or, (dF/dT)P = − S -----(equation-4)
We know that-
F = H − TS -----(equation-1)
or, F = E + PV − TS (as H = E + PV)
differentiating this equation we get-
dF = dE + PdV + VdP − TdS − SdT
or, dF = dq + VdP − TdS − SdT (as dq = dE + PdV)
or, dF = TdS + VdP − TdS − SdT (as dqrev/T = dS)
or, dF = VdP − SdT -----(equation-2)
at constant Temperature-
or, dF = VdP
or, (dF/dP)T = V -----(equation-3)
and at constant Pressure-
or, dF = − SdT
or, (dF/dT)P = − S -----(equation-4)
Free Energy Change of Expansion of an Ideal Gas
When a system undergo a reversible change, the change in free energy with temperature and pressure is given as-
dF = VdP − SdT
at constant temperature-
dF = VdP
or, dF = nRT.(dP/p) (as PV = nRT)
on integrating the above equation we get-
∫dF = nRT∫dP/P
or, ΔF = nRT lnP2/P1
or, ΔF = nRT lnV1/V2 (as P1V1 = P2V2 )
When a system undergo a reversible change, the change in free energy with temperature and pressure is given as-
dF = VdP − SdT
at constant temperature-
dF = VdP
or, dF = nRT.(dP/p) (as PV = nRT)
on integrating the above equation we get-
∫dF = nRT∫dP/P
or, ΔF = nRT lnP2/P1
or, ΔF = nRT lnV1/V2 (as P1V1 = P2V2 )
Enthalpy (H)
It is heat contained in the system measured at constant pressure. The sum of internal energy and pressure volume (PV) energy is known as enthalpy.
H = E + PV
(-----equation-1)
It is an extensive property and also a state function so depends only on initial and final state of the system.
So, change in enthalpy
ΔH = Hfinal − Hinitial
From equation-1-
ΔH = ΔE + Δ(PV) (-----equation-2)
or, ΔH = ΔE + PΔV + VΔP
at constant P-
ΔH = ΔE + PΔV (-----equation-3)
and at constant V-
ΔH = ΔE + VΔP (-----equation-4)
For chemical reactions, at constant temprature and pressure equation-2 becomes-
ΔH = ΔE + ΔngasRT (-----equation-5)
at constant P-
ΔH = qp
and at constant V-
ΔH = qv
so, equaton-5 becomes-
qp = qv + ΔngasRT (-----equation-6)
For endothermic reaction change in enthalpy is positive and for exothermic reaction it is negative.
ΔH = +ve for Endothermic Reaction
ΔH = −ve for Exothermic Reaction
It is heat contained in the system measured at constant pressure. The sum of internal energy and pressure volume (PV) energy is known as enthalpy.
H = E + PV
(-----equation-1)
It is an extensive property and also a state function so depends only on initial and final state of the system.
So, change in enthalpy
ΔH = Hfinal − Hinitial
From equation-1-
ΔH = ΔE + Δ(PV) (-----equation-2)
or, ΔH = ΔE + PΔV + VΔP
at constant P-
ΔH = ΔE + PΔV (-----equation-3)
and at constant V-
ΔH = ΔE + VΔP (-----equation-4)
For chemical reactions, at constant temprature and pressure equation-2 becomes-
ΔH = ΔE + ΔngasRT (-----equation-5)
at constant P-
ΔH = qp
and at constant V-
ΔH = qv
so, equaton-5 becomes-
qp = qv + ΔngasRT (-----equation-6)
For endothermic reaction change in enthalpy is positive and for exothermic reaction it is negative.
ΔH = +ve for Endothermic Reaction
ΔH = −ve for Exothermic Reaction
At 27°C the internal energy change of reaction H2(g) + Cl2(g) → 2HCl(g) is 2Cal. What is the enthalpy change of this reaction.
Hess' Law
The enthalpy change in a chemical or physical process is the same whether the process is carried out in a single step or in multiple steps. The purpose of Hess' law is to measure the enthalpies of neutralization for several acid-base reactions.
Let us consider a general chemical equation-
Reaction takes place in a single step-
A + B → D ΔH = Q
Reaction takes place in multiple steps-
A + B → C ΔH = Q1
C → D ΔH = Q2
So, according to Hess' law-
Q = Q1 + Q2
Applications
Followings are some important applications of Hess' law
Use to calculate heats of many reactions which do not take place directly.
Use to determine the bond enthalpies.
Use to calculate enthalpies of reactants and products.
It is useful to find out heat from extremely slow reactions.
It is useful to find out the Heat of reaction, Heat of transition, Lattice energy of the crystal, Heat of formation of intermediate compounds which are unstable.
The enthalpy change in a chemical or physical process is the same whether the process is carried out in a single step or in multiple steps. The purpose of Hess' law is to measure the enthalpies of neutralization for several acid-base reactions.
Let us consider a general chemical equation-
Reaction takes place in a single step-
A + B → D ΔH = Q
Reaction takes place in multiple steps-
A + B → C ΔH = Q1
C → D ΔH = Q2
So, according to Hess' law-
Q = Q1 + Q2
Applications
Followings are some important applications of Hess' law
Use to calculate heats of many reactions which do not take place directly.
Use to determine the bond enthalpies.
Use to calculate enthalpies of reactants and products.
It is useful to find out heat from extremely slow reactions.
It is useful to find out the Heat of reaction, Heat of transition, Lattice energy of the crystal, Heat of formation of intermediate compounds which are unstable.
