Question

Heat energy of 735J is given to a diatomic gas allowing the gas to expand at constant pressure Each gas molecule rotates around an internal axis but do not oscillate The increase in the intemal energy of the gas will be :

• A. 572J
• B. 735J
• C. 525J
• D. 441J

Hint:

For diatomic gases, rotational energy contributes \( \frac{3}{2} \) of the total energy increase during an expansion at constant pressure.

Answer 1

The Correct Option is C

To determine the increase in the internal energy of the diatomic gas when a specific amount of heat is added, we need to consider the principles of thermodynamics, specifically the first law of thermodynamics.

The first law of thermodynamics is given by:

\(Q = \Delta U + W\)

where \(Q\) is the heat supplied to the system, \(\Delta U\) is the change in internal energy, and \(W\) is the work done by the system.

Since the gas is expanding at constant pressure, the work done by the gas, \(W\), can be calculated using:

\(W = P \Delta V\)

For a diatomic gas, which neither oscillates nor vibrates and only rotates, its degrees of freedom is 5. When considering an ideal diatomic gas at constant pressure, the specific heat capacities are:

\(C_p = \frac{7}{2} R\)

\(C_v = \frac{5}{2} R\)

The relationship between \(C_p\) and \(C_v\) gives us \(\Delta U\) in terms of \(Q\):

At constant pressure, the formula can be simplified to:

\(\Delta U = nC_v\Delta T = (Q - W)\)

But we need to focus on the question asked: \(\Delta U = \frac{5}{7}Q\) (since pressure is constant and work done is proportional to the pressure-volume change).

Given \(Q = 735 \, \text{J}\), we can substitute into this formula:

\(\Delta U = \frac{5}{7} \times 735 \, \text{J}\)

\(\Delta U = 525 \, \text{J}\)

Therefore, the increase in the internal energy of the gas is \(525 \, \text{J}\).

This matches the correct option provided: 525J.