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: Understanding the Concept
In an adiabatic process \(\Delta Q=0\), meaning no heat flows in or out.

Step 2: Molar heat capacity
\(C=\dfrac{\Delta Q}{n\Delta T}=0\) because \(\Delta Q=0\) while \(\Delta T\) is not zero.

Step 3: Check the other statements
First law gives \(W=-\Delta U\), so the work done by the gas equals the decrease in internal energy, not the increase.
Internal energy depends on temperature, so it increases when temperature increases.

Step 4: Compare the options
Only option (C) is true.

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