Points to Remember: Thermodynamics | Physical Chemistry PDF Download

Points to be Remembered

1. Some Important Terms:
A. System: It is the part of the universe which is taken into consideration. It is classified into three categories depending upon the transfer of mass and energy between the system and surroundings.

• Open System: If mass and energy are exchanged between system and surroundings then that system is called open system. Example - A cup of hot tea.
• Closed System: If only energy is exchanged between system and surroundings then that system is called closed system. Example - Thermometer.
• Isolated System: If neither mass nor energy are exchanged between system and surroundings then that system is called isolated system.
  Example - Thermo flask.

B. Surroundings: The rest part of the universe is called surroundings.

C. Properties: Thermodynamic properties are classified into two categories-

• Extensive Property: The properties which are dependent on the mass of the system are known as extensive properties.
  Example - Volume, Internal energy, Enthalpy, Entropy, Gibbs' free energy etc.
• Intensive Property: The properties which are independent on the mass of the system are known as intensive property.
  Example - Molar properties such as molar internal energy, molar enthalpy, molar entropy, molar Gibbs' free energy, density etc.

D. Processes:

• Isothermal Process: The process in which temperature is kept constant throughout the whole process is called isothermal process.
• Isobaric Process: The process in which pressure is kept constant throughout the whole process is called isobaric process.
• Isochoric Process: The process in which volume is kept constant throughout the whole process is called isochoric process.
• Cyclic Process: The process in which a system after undergoing through a series of changes comes back to its initial state is known as cyclic process.
• Adiabatic Process: The process in which the heat change in constant is called adiabatic process.

2. Some Important Formulas:

• Internal energy change is given by: ΔE = nCv,m(T_f - T_i)
• Enthalpy change is given by: ΔH = nC_P,m(T_f - T_i)
• Reversible work is given by: W_rev = -nRTln(V_f/V_i)
• Irreversible work is given by: W_irr = -P_ex(V_f - V_i)
• Entropy change for a reversible process is given by: ΔS = nRln(V_f/V_i) + nC_v,mln(T_f/T_i). Also, ΔS = nRln(P_i/P_f) + nC_p,mln(T_f/T_i).
• Entropy change for isothermal process is given by : ΔS = nRln(V_f/V_i). Also, ΔS = nRln(P_i/P_f)
• Entropy change for isobaric process is given by : ΔS = nC_p,mln(T_f/T_i).
• Entropy change in isochoric process is given by : ΔS = nC_v,mln(T_f/T_i).
• The efficiency of a Carnot engine is given by : η = 1 - T₁/T₂ = 1 - Q₁/Q₂
• The relationship between the internal energy change and enthalpy change is given by : ΔH = ΔE + ΔnRT

3. Maxwell's Relations:

The four fundamental equations of states of thermodynamics:
dG = -SdT + VdP ........ (1)
dA = -SdT - PdV ......... (2)
dH = TdS + VdP ...........(3)
and dU = TdS - PdV .............(4)

• (dS/dP}_T = (dV/dT)_P:

Differentiating equation (1) with respect to T at constant P, we have:
(dG/dT)_P = -S .......... (5)
Differentiating equation (5) with respect P to at constant T, we have:
[d²G/dPdT]_T = (dS/dP)_T ........ (6)
Also, differentiating equation (1) with respect to P at constant T, we have:
(dG/dP)_T = V .......... (7)
Differentiating equation (7) with respect to T at constant P, we have:
[d²G/dTdP]_P = (dV/dT)P ......... (8)
As G is a state function, [d²G/dPdT]_T = [d²G/dTdP]_p
(dS/dP)_T = (dV/dT)_P

• (dS/dV)_T = (dP/dT)v:

Differentiating equation (2) with respect to T at constant V, we have:
(dA/dT)v = -S ........ (9)
Differentiating equation (9) with respect to V at constant T, we have:
[d²A/d VdT]_T = -(dS/dV)_T ........ (10)
Also, differentiating equation (2) with respect to V at constant T, we have:
(dA/dV)_T = -P ........ (11)
Differentiating equation (11) with respect to T at constant V, we have:
[d²A/dTdV]_v = -(dP/dT)v ......... (12)
As A is also a state function, [d²A/dVdT]_T = [d²A/dTdV]_v

(dS/dV)_T= (dP/dT)_v

• (dT/dP)s = (dV/dS)P:

Differentiating equation (3) with respect to S at constant P, we have:
(dH/dS)_p = T .......... (13)
Differentiating equation (13) with respect to P at constant S, we have:
[d²H/dPdS]_s = (dT/dP)_s ............ (14)
Also, differentiating equation (3) with respect to P at constant S, we have:
(dH/dP)_s = V ............ (15)
Differentiating equation (15) with respect to S at constant P, we have:
[d²H/dSdP]_P = (dV/dS)_P ............ (16)
As H is also a state function, [d²H/dPdS]_s = [d²H/dSdP]_P
(dT/dP)s = (dV/dS)P

• (dT/dV)s = -(dP/dS)v:

Differentiating equation (4) with respect to S at constant V, we have:
(dU/dS)v = T ........ (17)
Differentiating equation(17) with respect to V at constant S, we have:
[d²U/dVdS]_s = (dT/dV)_s ..........(18)
Also, differentiating equation (4) with respect to V at constant S, we have:
(dU/dV)s = -P ..........(19)
Differentiating equation (19) with respect to S at constant V, we have:
[d²U/dSdV]_v = -(dP/dS)_v
As U is also a state function, [d²U/dVdS]_s = [d²U/dSdV]_v
(dT/dV)_s = -(dP/dS)_v