Question

In an adiabatic process, which one of the following statement is true ?

• A. The molar heat capacity is infinite
• B. Work done by the gas equals the increase in internal energy
• C. The molar heat capacity is zero
• D. The internal energy of the gas decreases as the temperature increases

Hint:

In an adiabatic process no heat is exchanged, so the heat required per unit temperature change is zero.

Answer 1

The Correct Option is C

Step 1: Apply the first law
$0=\Delta U+W$, so $W=-\Delta U$.

Step 2: Eliminate options
Option (B) has the wrong sign and option (D) contradicts $U\propto T$. Infinite heat capacity belongs to an isothermal process.

Step 3: Select
Since no heat is exchanged, the heat capacity is zero, option (C).

Final Answer:
The molar heat capacity is zero. \[ \boxed{\text{(C) }\text{The molar heat capacity is zero}} \]