JEE Advanced · Chemistry · 6. Thermodynamics (C)
Consider the following volume-temperature \((\mathrm{V}-\mathrm{T})\) diagram for the expansion of 5 moles of an ideal monoatomic gas.
Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence \(\mathbf{X} \rightarrow \mathbf{Y} \rightarrow \mathbf{Z}\) is ________.
[Use the given data: Molar heat capacity of the gas for the given temperature range, \(\mathrm{C}_{\mathrm{V}, \mathrm{m}}=12 \mathrm{~J} \mathrm{~K}^{-1}\) \(\mathrm{mol}^{-1}\) and gas constant, \(\left.\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]\)
- A 8120
- B 854
- C 2638
- D 1245
Answer & Solution
Correct Answer
(A) 8120
Step-by-step Solution
Detailed explanation
For ideal gas
\(\Delta \mathrm{H}=\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}\)
\(\because \quad \mathrm{C}_{\mathrm{P}}=\mathrm{C}_{\mathrm{V}}+\mathrm{R}=12+8.3=20.3 \mathrm{~J} / \mathrm{K}\)-mole
\(\therefore \Delta H=5 \times 20.3 \times(415-335)\)
\(\Delta H=8120\) Joule
\(\Delta \mathrm{H}=\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}\)
\(\because \quad \mathrm{C}_{\mathrm{P}}=\mathrm{C}_{\mathrm{V}}+\mathrm{R}=12+8.3=20.3 \mathrm{~J} / \mathrm{K}\)-mole
\(\therefore \Delta H=5 \times 20.3 \times(415-335)\)
\(\Delta H=8120\) Joule
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