Question:
Consider the following volume−temperature (V−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 X→Y→Z is ______.
[Use the given data: Molar heat capacity of the gas for the given temperature range, CV,m = 12 J K−1mol−1 and gas constant, R=8.3 JK−1 mol−1]
Consider the following volume−temperature (V−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 X→Y→Z is ______.
[Use the given data: Molar heat capacity of the gas for the given temperature range, CV,m = 12 J K−1mol−1 and gas constant, R=8.3 JK−1 mol−1]
Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence X→Y→Z is ______.
[Use the given data: Molar heat capacity of the gas for the given temperature range, CV,m = 12 J K−1mol−1 and gas constant, R=8.3 JK−1 mol−1]
Updated On: Mar 7, 2025
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Correct Answer: 8120
Solution and Explanation
Step 1: Understanding Enthalpy Change for an Ideal Gas
The change in enthalpy (\(\Delta H\)) for an ideal gas is given by:
\[ \Delta H = n C_P \Delta T \]
where \( C_P = C_V + R \) for a monoatomic gas.
Step 2: Calculating \( C_P \)
\[ C_P = 12 + 8.3 = 20.3 \text{ J K}^{-1} \text{mol}^{-1} \]
Step 3: Determining the Temperature Change
From the diagram:
\[ \Delta T = T_Z - T_X = 415K - 335K = 80K \]
Step 4: Computing Enthalpy Change
\[ \Delta H = 5 \times 20.3 \times 80 \]
\[ = 8120 \text{ J} \]
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