# Thermodynamics Questions and Answers – Energy Equation-1

This set of Thermodynamics Multiple Choice Questions & Answers (MCQs) focuses on “Energy Equation-1”.

1. For a system which undergoes an infinitesimal reversible process between two equilibrium states, the change in internal energy is
a) dU = pdV – TdS
b) dU = TdS + pdV
c) dU = TdS – pdV
d) dU = -TdS – pdV

Explanation: This is a basic equation for change in internal energy for an infinitesimal reversible process.

2. The energy equation is given by
a) (∂U/∂V) = T*(∂p/∂T) + p
b) (∂U/∂V) = T*(∂p/∂T) – p
c) (∂U/∂V) = -T*(∂p/∂T) – p
d) (∂U/∂V) = p – T*(∂p/∂T)

Explanation: We get this equation when we substitute the first TdS equation in dU = TdS – pdV and U is taken as a function of T and V.

3. If temperature is constant, internal energy does not change.
a) true
b) false

Explanation: U does not change with change in V if the temperature is constant.

4. If the temperature is constant, internal energy
a) changes with change in p
b) changes with change in V
c) changes with change in both p and V
d) does not change with change in p or V

Explanation: The internal energy of an ideal gas is a function of temperature only.

5. The equation dU=Cv*dT holds good for
a) any process for an ideal gas, even when the volume changes
b) for other substances it is true only when the volume is constant
c) both of the mentioned
d) none of the mentioned

Explanation: For an ideal gas, pV=nRT and T(∂p/∂T) – p =0.

6. Thermal radiation in equilibrium with enclosing walls possesses an energy that depends on volume and temperature.
a) true
b) false

Explanation: It depends on temperature and volume only and not on any other thermodynamic property.

7. If the temperature is constant, enthaply
a) changes with change in p
b) changes with change in V
c) changes with change in both p and V
d) does not change with change in p or V

Explanation: The enthaply of an ideal gas is a function of temperature only and does not depend on pressure and volume.

8. The equation dH=Cp*dT holds good for
a) any process for an ideal gas, even when the pressure changes
b) for other substances it is true only when the pressure is constant
c) both of the mentioned
d) none of the mentioned

Explanation: For an ideal gas, pV=nRT and V – T(∂V/∂T) =0.

9. If u is the energy density then pressure(p) exerted by the black-body radiation in an enclosure is
a) u/2
b) u/3
c) u/4
d) u

Explanation: Here energy density, u=U/V.

10. The Stefan-Boltzmann law is given by
a) u = b*(T2)
b) u = b*(T3)
c) u = b*(T4)
d) u = b*T

Explanation: Here b is a constant and this equation is derived from the basic energy equation.

11. For a reversible isothermal change of volume, heat to be supplied reversibly to keep temperature constant is given by
a) Q = (4/3)b*(T4)*(ΔV)
b) Q = (2/3)b*(T2)*(ΔV)
c) Q = (1/3)b*(T)*(ΔV)
d) none of the mentioned

Explanation: This relation comes from the first TdS equation.

12. If the temperature is half the original temperature, the volume of black-body radiation is to be ____ adiabatically ____ times its original volume for radiation to remain at equilibrium.
a) decreased, four
b) decreased, eight
c) increased, four
d) increased, eight

Explanation: This comes form the relation V*(T^3) = constant.

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