Question

For a monoatomic gas, work done at constant pressure is W. The heat supplied at constant volume for the same rise in temperature of the gas is

• A. \( \frac{W}{2} \)
• B. \( \frac{3W}{2} \)
• C. W
• D. \( \frac{5W}{2} \)

Hint:

The heat supplied at constant volume for a monoatomic gas is related to the work done at constant pressure by the ratio of specific heats.

Answer 1

The Correct Option is D

For an ideal monoatomic gas, the relationship between heat supplied, work done, and the temperature change is given by:

\[ Q = W + \Delta U \] where \( Q \) is the heat supplied, \( W \) is the work done, and \( \Delta U \) is the change in internal energy. In a thermodynamic process, the change in internal energy is related to the temperature change. For an ideal monoatomic gas, the change in internal energy is given by \( \Delta U = \frac{3}{2} n R \Delta T \), where \( n \) is the number of moles of the gas, \( R \) is the ideal gas constant, and \( \Delta T \) is the temperature change.

At constant volume, the work done is zero because there is no change in volume. Therefore, the heat supplied equals the change in internal energy in this case, so \( Q = \Delta U \).

For constant pressure, the heat supplied is the sum of the work done and the change in internal energy. The work done at constant pressure is \( W = P \Delta V \), and the heat supplied is related to this by the equation \( Q = W + \Delta U \). For a monoatomic ideal gas at constant pressure, the total heat supplied is \( Q = \frac{5}{2} W \), which is a well-known relationship.

Hence, the correct answer is (d).