Two moles of ideal gas undergo isothermal expansion from volume V to 2V at temperature T. The work done during the expansion is

The correct answer is Option 2. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q99 – AP-EAMCET 2026

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Two moles of ideal gas undergo isothermal expansion from volume

V

2 V

at temperature

T

. The work done during the expansion is

Clue 1 of 3: Isothermal Process Definition

An isothermal process is a thermodynamic process that occurs at a constant temperature. For an ideal gas undergoing such a process, the change in internal energy is zero.

🧠 Full Solution Path

Step 1: Identify the Process and Given Parameters✦ Active

The problem describes an isothermal expansion of an ideal gas. We are given the following parameters:

Number of moles ( $n$ ) = $2$

Initial volume ( $V_{i n i t i a l}$ ) = $V$

Final volume ( $V_{f i n a l}$ ) = $2 V$

Temperature = $T$ (constant)

Gas constant = $R$

💡 Teacher's Secret Hint

Always start by listing all the knowns and identifying the type of thermodynamic process involved, as this dictates the formula to use.

Step 2: Recall the Formula for Work Done in Isothermal Expansion○ Expand

For a reversible isothermal expansion of an ideal gas, the work done by the gas is given by the formula:

W = n R T \ln (\frac{V_{f i n a l}}{V_{i n i t i a l}})

💡 Teacher's Secret Hint

Remember that work done BY the system is positive in this convention, while work done ON the system would have a negative sign.

Step 3: Substitute the Given Values into the Formula○ Expand

Substitute the identified values into the work formula:

W = (2) R T \ln (\frac{2 V}{V})

💡 Teacher's Secret Hint

Be careful with the number of moles ( $n$ ) and ensure it's correctly substituted. In some problems, $n$ might be implicitly 1 if not specified.

Step 4: Simplify the Expression to Find the Work Done○ Expand

Simplify the expression by canceling $V$ from the ratio:

W = 2 R T \ln (2)

This result corresponds to option 2.

💡 Teacher's Secret Hint

Ensure you correctly evaluate the natural logarithm of the volume ratio. $\ln (2)$ is a common value in such problems.

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Physics Question 99 – AP-EAMCET 2026

Clue 1 of 3: Isothermal Process Definition

🧠 Full Solution Path