Question

If the temperature of $2$ moles of krypton gas is increased from $-11^\circ$C to $89^\circ$C at constant volume, then (specific heat at constant volume of krypton is $C_V$)

• A. work done on the gas is not zero
• B. internal energy is not changed
• C. work is done by the gas
• D. amount of heat added is $200\,C_V$
• E. internal energy is increased by $100\,C_V$

Hint:

For constant volume processes: - $Q = nC_V \Delta T$ - No work is done ($W = 0$)

Answer 1

The Correct Option is D

Concept: At constant volume: \[ Q = nC_V \Delta T \] Also, work done $W = 0$.

Step 1: Calculate temperature change.
\[ \Delta T = 89 - (-11) = 100^\circ \text{C} = 100\ \text{K} \]

Step 2: Substitute values.
\[ Q = nC_V \Delta T = 2 \times C_V \times 100 \]

Step 3: Simplify.
\[ Q = 200\,C_V \]