Question

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

• 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.

Answer 1

Answer: (A), (B), (C), (D)

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
$\Delta U=n{C}_V(T_2-T_1).......\left(1\right)$
So, $\Delta U$ only depends on $T_2$ and $T_1$

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

For an isothermal process, $\Delta T=0$
$\therefore$ From equation $\left(1\right)$, we can say that $\Delta U=0$
Thus, options (a) , (b) , (c) and (d) are correct answers.