Question

1 mole of oxygen is heated at constant pressure (1 atm) from $ 20^\circ C $ to $ 80^\circ C $, and then cooled from $ 80^\circ C $ to $ 20^\circ C $ at constant volume. If $ C_p = 7.03 \, \text{cal/mol}^\circ\text{C} $ and $ C_v = 5.04 \, \text{cal/mol}^\circ\text{C} $, what is the difference between the heat supplied and the heat rejected?

• A. \( 302.4 \, \text{cal} \)
• B. \( 119.4 \, \text{cal} \)
• C. \( 421.8 \, \text{cal} \)
• D. \( 60.0 \, \text{cal} \)

Hint:

Always use the correct heat capacity based on the process type: use \( C_p \) for constant pressure and \( C_v \) for constant volume.

Answer 1

The Correct Option is B

Heat supplied at constant pressure: \[ Q_s = n C_p \Delta T = 1 \times 7.03 \times (80 - 20) = 421.8 \, \text{cal} \] Heat rejected at constant volume: \[ Q_r = n C_v \Delta T = 1 \times 5.04 \times (80 - 20) = 302.4 \, \text{cal} \] Difference: \[ Q_s - Q_r = 421.8 - 302.4 = 119.4 \, \text{cal} \]