Consider the following volume-temperature (V - T) diagram for the expansion of 5 moles of an ideal monoatomic gas. (see diagram) 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, $\mathrm{C}_{\mathrm{V},\mathrm{m}}=12~\mathrm{J~K}^{-1}\mathrm{~mol}^{-1}$ and gas constant, $\mathrm{R}=8.3~\mathrm{J~K}^{-1}\mathrm{~mol}^{-1}$]

JEE Advanced · 2024 · 26 May 2024 · Paper 1 · Chemical Thermodynamics

Consider the following volume-temperature (V - T) diagram for the expansion of 5 moles of an ideal monoatomic gas.

(see diagram)

Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence

X \to Y \to Z

is ____.
[Use the given data: Molar heat capacity of the gas for the given temperature range,

C_{V, m} = 12 J K^{- 1} mol^{- 1}

and gas constant,

R = 8.3 J K^{- 1} mol^{- 1}

]

Answer: 8120

Solution

For an ideal gas, the change in enthalpy depends only on temperature:

Δ H = n C_{P} Δ T

. Since

C_{P} = C_{V} + R = 12 + 8.3 = 20.3

J/(K·mol), and from the diagram

Δ T = 415 - 335 = 80

K, we have

Δ H = 5 \times 20.3 \times 80 = 8120

Joule.

JEE Advanced · 2024 · 26 May 2024 · Paper 1 · Integer answer

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