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Question

For an ideal gas, choose the correct option(s).

A
Change in internal energy only depends on the initial and final temperatures.
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B
Change in internal energy of the gas and work done by the gas are equal in magnitude in an adiabatic process.
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C
Internal energy does not change in an isothermal process.
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D
No heat is added or removed in an adiabatic process.
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Solution

The correct options are
A Change in internal energy only depends on the initial and final temperatures.
B Change in internal energy of the gas and work done by the gas are equal in magnitude in an adiabatic process.
C Internal energy does not change in an isothermal process.
D No heat is added or removed in an adiabatic process.
For any thermodynamic process, the change in internal energy of n moles of an ideal gas is given by
ΔU=nCV(T2T1) .......(1)
So, ΔU only depends on T2 and T1

First law of thermodynamics for a process states that,
ΔQ=ΔU+ΔW
For an adiabatic process, we know that
ΔQ=0
i.e no heat is added or taken from the ideal gas during an adiabatic process.
0=ΔU+ΔW
or |ΔU|=|ΔW|
i.e Magnitude of change in internal energy and work done are the same.

For an isothermal process, ΔT=0
From equation (1), we can say that ΔU=0
Thus, options (a) , (b) , (c) and (d) are correct answers.

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