Question

The heat required to increase the temperature of 4 moles of a mono-atomic ideal gas from \( 273^\circ C \) to \( 473^\circ C \) at constant volume is

• A. \( 1600R \)
• B. \( 600R \)
• C. \( 1200R \)
• D. \( 400R \)

Hint:

For mono-atomic ideal gas at constant volume, always use \( C_V = \frac{3R}{2} \).

Answer 1

The Correct Option is C

Step 1: Use heat formula at constant volume.
At constant volume, heat supplied is:
\[ Q = nC_V\Delta T \]

Step 2: Write molar specific heat for mono-atomic gas.
For a mono-atomic ideal gas:
\[ C_V = \frac{3R}{2} \]

Step 3: Write number of moles.
\[ n = 4 \]

Step 4: Calculate temperature change.
\[ \Delta T = 473 - 273 \]
\[ \Delta T = 200 \]

Step 5: Substitute values in formula.
\[ Q = 4 \times \frac{3R}{2} \times 200 \]

Step 6: Simplify the expression.
\[ Q = 2 \times 3R \times 200 \]
\[ Q = 1200R \]

Step 7: Final Answer.
\[ \boxed{1200R} \]