Kirchhoff's Equation And Heat Capacity

Question

At constant pressure, the molar heat capacity of nitrogen gas $(C_p)$ is 29.1 J/mol·K. How much heat is required to raise the temperature of 2 moles of nitrogen from 300 K to 500 K at constant pressure?

RankGuru · Accepted Answer

At constant pressure, the heat absorbed by a substance is given by $q_p = nC_p\Delta T$, which equals the enthalpy change $\Delta H$. This relationship follows directly from the definition of enthalpy and the first law of thermodynamics. Here $n = 2$ mol, $C_p = 29.1$ J/mol·K, and $\Delta T = 500 - 300 = 200$ K. Therefore, $q_p = 2 \times 29.1 \times 200 = 11640$ J. Option 5820 J is the heat for only 1 mole — it omits the factor of 2 for the number of moles. Option 23280 J doubles the answer incorrectly, possibly due to using $\Delta T = 400$ K. Option 2910 J corresponds to heating only 0.5 mol. This is a straightforward application of NCERT heat capacity at constant pressure. Plausibility check: nitrogen is diatomic and its $C_p$ is approximately $\frac{7}{2}R \approx 29.1$ J/mol·K, which is consistent with the equipartition theorem, confirming the data is physically reasonable.

Kirchhoff's Equation And Heat Capacity

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