Question

An ideal gas undergoes an isothermal process. Which of the following statements are true? (i) No heat is added to or removed from the gas. (ii) The internal energy of the gas does not change. (iii) The average kinetic energy of the molecules does not change.

(a) (i) only.

(b) (i) and (ii) only.

(c) (i) and (iii) only.

(d) (ii) and (iii) only.

(e) (i), (ii), and (iii).

(f) None of the above.

Short answer

The correct option is (d).

Step-by-step solution

Concept

By the first law of thermodynamics,$\mathrm{\Delta }U=Q-W$.

For the isothermal process, the change in internal energy is$\mathrm{\Delta }U=0$.

Explanation

For the isothermal process,

$\begin{array}{c}0=Q-W\\ Q=W.\end{array}$

In the isothermal process, the work done equals the heat supplied to the system. It means that the heat added to the system is equal to the work done. Also, the change in internal energy is zero during the isothermal process.

The kinetic energy of the gas molecules depends on the internal energy of the gas. As the internal energy of the gas does not change, the kinetic energy of the gas molecules also does not change.

Hence, options (ii) and (iii) are correct.