Question:
At constant temperature, one mole of an ideal gas of volume 2L was expanded to 100 L against an external pressure of 1 atm under reversible conditions. What is the change in internal energy? \((1 L atm=101.3~J; log~5=0.7)\)
At constant temperature, one mole of an ideal gas of volume 2L was expanded to 100 L against an external pressure of 1 atm under reversible conditions. What is the change in internal energy? \((1 L atm=101.3~J; log~5=0.7)\)
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For any isothermal process involving an ideal gas, \(\Delta U = 0\) and \(\Delta H = 0\) because both of these state functions depend solely on temperature.
Updated On: Jun 8, 2026
- Zero
- 793.2 J
- 3266 J
- 326.6 J
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The Correct Option is A
Solution and Explanation
Concept:
The internal energy (\(U\)) of an ideal gas is a state function that depends exclusively on the temperature (\(T\)) of the system. According to the kinetic molecular theory, for an ideal gas, the internal energy is directly proportional to the temperature.
Step 1: Analyze the thermodynamic process.
The problem states that the gas is expanded at a "constant temperature." This identifies the process as an isothermal expansion.
Step 2: Determine the change in temperature (\(\Delta T\)).
Since the temperature remains constant throughout the entire expansion process, the change in temperature (\(\Delta T\)) is equal to zero.
Step 3: Calculate the change in internal energy (\(\Delta U\)).
For an ideal gas, the change in internal energy is given by the formula \(\Delta U = n C_v \Delta T\). Since \(\Delta T = 0\), it follows that \(\Delta U = 0\). Therefore, the internal energy does not change during this process.
Step 1: Analyze the thermodynamic process.
The problem states that the gas is expanded at a "constant temperature." This identifies the process as an isothermal expansion.
Step 2: Determine the change in temperature (\(\Delta T\)).
Since the temperature remains constant throughout the entire expansion process, the change in temperature (\(\Delta T\)) is equal to zero.
Step 3: Calculate the change in internal energy (\(\Delta U\)).
For an ideal gas, the change in internal energy is given by the formula \(\Delta U = n C_v \Delta T\). Since \(\Delta T = 0\), it follows that \(\Delta U = 0\). Therefore, the internal energy does not change during this process.
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