Question

Identify the characteristics of an adiabatic process in a monatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from $ T_1 $ to $ T_2 $ is proportional to $ (T_2 - T_1) $. Choose the correct answer from the options given below:

• A. (A), (C), (D) only
• B. (A), (C), (E) only
• C. (B), (E) only
• D. (B), (D) only

Hint:

In an adiabatic process, internal energy change is equal to the work done, and the work is proportional to the change in temperature.

Answer 1

The Correct Option is C

For an adiabatic process, the heat exchanged \( Q = 0 \), hence, the change in internal energy is equal to the work done on or by the system: \[ Q = \Delta U + W = 0 \implies \Delta U = - W \] For an adiabatic process, the work done \( W \) is proportional to the change in temperature. Also, we know that: \[ W = -n C_V \Delta T \quad \text{or} \quad |W| = n C_V \Delta T \propto T_2 - T_1 \] Thus, both (B) and (E) are correct, making option (3) the correct answer.