Question

In an isothermal expansion
A. Internal energy of the gas decreases
B. Internal Energy of the gas increases
C. Internal Energy remains unchanged
D. Average kinetic energy of gas molecule decreases

Answer 1

Hint: In an Isothermal process in a thermodynamic system, the temperature is constant and at a constant temperature, the effect on the internal energy can be predicted by using the expression $U = f\left( T \right)$ as internal energy depends directly on the temperature for a perfect gas.

Complete step by step solution:
An isothermal process in thermodynamics is defined as the process during which the temperature $T$ of a system remains constant that’s why it is also referred to as a constant-temperature process. That is in an Isothermal process, $T = \text{constant}$ and $\text{Change in Temperature} = \Delta T = 0$

Since the relationship between internal energy and temperature is: -
$U = f\left( T \right)$ and as $T = \text{constant}$
$ \Rightarrow U = \text{constant}$ which means options (A) and (B) are incorrect.
Graphically, the above situation is represented as: -

Additionally, because the average kinetic energy of the gas molecules is proportional to its average temperature and because that temperature is constant during isothermal expansion, the average kinetic energy of the gas molecules will also remain constant, making option (D) incorrect. Thus, in an isothermal expansion, Internal Energy remains unchanged.

Hence, the correct option is C.

Note: In this problem, to determine which statement is correct with respect to an isothermal thermodynamic process, use $\Delta T = 0$ and hence, analyze every given option of internal energy and average kinetic energy of the gas molecule carefully to give an answer with a precise explanation.