Question 7

Heat energy of 735 J 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 internal energy of the gas will be:

Heat energy $$Q = 735$$ J given to a diatomic gas at constant pressure. The gas molecules rotate but do not oscillate.

Diatomic gas with rotation, no oscillation: $$f = 5$$ (3 translational + 2 rotational).

$$C_v = \frac{5}{2}R$$ $$C_p = \frac{7}{2}R$$

At constant pressure: $$Q = nC_p\Delta T$$ and $$\Delta U = nC_v\Delta T$$.

$$\frac{\Delta U}{Q} = \frac{C_v}{C_p} = \frac{5/2}{7/2} = \frac{5}{7}$$ $$\Delta U = \frac{5}{7} \times Q = \frac{5}{7} \times 735 = 525 \text{ J}$$

The answer is Option A: 525 J.

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