# Thermodynamics Questions and Answers – Difference in Heat Capacities and their Ratio

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This set of Basic Thermodynamics questions and answers focuses on “Difference in Heat Capacities and their Ratio”.

1. What do we get on equating the first and second TdS equations?
a) Cp-Cv = T*(∂T/∂p)*(∂V/∂T)
b) Cp-Cv = T*(∂p/∂T)*(∂V/∂T)
c) Cp+Cv = T*(∂p/∂T)*(∂V/∂T)
d) none of the mentioned

Explanation: This is the relation we get on equating first and second TdS equations.

2. Consider the equation Cp-Cv = -T*(∂p/∂V)(∂V/∂T)2 , which of the following is correct?
a) (∂V/∂T)2 is always positive
b) (∂p/∂V) for any substance is negative
c) (Cp-Cv) is always positive
d) all of the mentioned

Explanation: From this we can conclude that, Cp is always greater than Cv.

3. When do we have the condition Cp=Cv?
a) as T approaches 0K, Cp tends to approach Cv
b) when (∂V/∂T)=0, Cp=Cv
c) both of the mentioned are correct
d) none of the mentioned are correct

Explanation: These facts come from the equation Cp-Cv = -T*(∂p/∂V)(∂V/∂T)2.

4. For an ideal gas,
a) Cp-Cv = R
b) Cp-Cv = mR
c) Cp=Cv
d) all of the mentioned

Explanation: This comes from the ideal gas equation, pV=mRT.

5. The volume expansivity and isothermal compressibility is defined as
a) volume expansivity = (1/V)*(∂V/∂T) at p and isothermal compressibility = (-1/V)*(∂V/∂T) at T
b) volume expansivity = (1/V)*(∂V/∂T) at p and isothermal compressibility = (-1/V)*(∂V/∂T) at T
c) volume expansivity = (1/V)*(∂V/∂T) at p and isothermal compressibility = (-1/V)*(∂V/∂T) at T
d) none of the mentioned

Explanation: These two terms are used for better representation of the original equation.

6. The equation Cp-Cv = -T*(∂p/∂V)(∂V/∂T)2 can also be expressed as
a) Cp-Cv = T*V*(isothermal compressibility)2 / (volume expansivity)
b) Cp-Cv = T*V*(isothermal compressibility) / (volume expansivity)
c) Cp-Cv = T*V*(volume expansivity)2 / (isothermal compressibility)
d) Cp-Cv = T*V*(volume expansivity) / (isothermal compressibility)

Explanation: This comes from the equation Cp-Cv = -T*(∂p/∂V)(∂V/∂T)2 when we use volume expansivity and isothermal compressibility in it.

7. At constant entropy, the two TdS equations give us the relation
a) Cp+Cv = 0
b) Cp=Cv
c) Cp-Cv = mR
d) Cp/Cv = ɣ

Explanation: This relation is obtained on dividing the two TdS equations.

8. The slope of an isentrope is ____ the slope of an isotherm on p-v diagram.
a) less than
b) greater than
c) equal to
d) less than or equal to

Explanation: This comes from the fact that ɣ>1.

9. Work done in reversible and isothermal compression is ____ the work done in reversible and adiabatic compression.
a) equal to
b) greater than
c) less than
d) less than or equal to

Explanation: We get this from the p-v diagram for compression work in different reversible processes.

10. Isothermal compression requires minimum work.
a) true
b) false

Explanation: This is because work in isothermal is less than the work in adiabatic process and that of polytropic process lies in between these values.

11. Which of the following relation gives ɣ .
b) isothermal compressibility * adiabatic compressibility
c) adiabatic compressibility / isothermal compressibility
d) isothermal compressibility / adiabatic compressibility 