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When 300 J of heat given to an ideal gas with $$C_{p}= \frac{7}{2}R$$ its temperature raises from $$20^{\circ}C$$ to $$50^{\circ}C$$ keeping its volume constant. The millimoles of the gas is (approximately) __ . (R = 8.314 J/mol.K)
Correct Answer: 481
For the ideal gas, $$C_v = C_p - R = \dfrac{7}{2}R - R = \dfrac{5}{2}R$$. At constant volume, $$Q = nC_v\Delta T$$. With $$Q = 300$$ J, $$\Delta T = 50 - 20 = 30$$ K, and $$R = 8.314$$ J/mol K:
$$300 = n \times \dfrac{5}{2} \times 8.314 \times 30 \implies n = \dfrac{300}{623.55} \approx 0.481$$ mol.
The answer is $$\boxed{481}$$.
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