Question

In a reversible adiabatic expansion of an ideal gas:

• A. The temperature of the gas remains constant
• B. The gas does work without heat exchange with the surroundings
• C. Heat is absorbed by the gas to perform work
• D. The process occurs at constant pressure

Hint:

In a reversible adiabatic process, remember: no heat exchange occurs (\( Q = 0 \)), and the gas does work by consuming its internal energy, leading to cooling.

Answer 1

The Correct Option is B

Step 1: An adiabatic process is defined as one in which no heat is exchanged between the system and its surroundings (\( Q = 0 \)).
Step 2: In a reversible adiabatic expansion, the gas performs work by pushing against a piston or external resistance, and since no heat enters or leaves the system, the energy required to do work must come from the internal energy of the gas.
Step 3: This results in a decrease in the internal energy and hence a decrease in the temperature of the gas. The relationship for an adiabatic process in an ideal gas is: \[ PV^\gamma = \text{constant} \quad \text{and} \quad TV^{\gamma-1} = \text{constant} \] where \( \gamma = \frac{C_P}{C_V} \) is the adiabatic index.
Why the other options are incorrect:

• (A) Temperature decreases, it does not remain constant (that would be isothermal).
• (C) No heat is absorbed; \( Q = 0 \) by definition.
• (D) Pressure is not constant; it decreases as the gas expands.