Kirchhoff's Equation And Heat Capacity
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?
Select the correct option:
Solution
11640 J
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.
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About This Question
- Subject
- chemistry
- Chapter
- chemical thermodynamics
- Topic
- kirchhoff's equation and heat capacity
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
11640 J
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.
This easy difficulty chemistry question is from the chapter chemical thermodynamics, covering the topic of kirchhoff's equation and heat capacity. It appeared in the 2025 exam.
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