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? \((1 L atm=101.3~J; log~5=0.7)\)

• A. Zero
• B. 793.2 J
• C. 3266 J
• D. 326.6 J

Hint:

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.

Answer 1

The Correct Option is A

Step 1: Recall what internal energy depends on.
For an ideal gas, internal energy depends only on temperature. It does not care about volume or pressure.
Step 2: Read the key word.
The problem says the expansion happens at constant temperature. So this is an isothermal change.
Step 3: Find the temperature change.
Because temperature stays fixed from start to end, $\Delta T=0$.
Step 4: Use the internal energy formula.
For an ideal gas $\Delta U=nC_v\Delta T$.
Step 5: Plug in the zero.
Since $\Delta T=0$, the whole product is zero, so $\Delta U=0$.
Step 6: Read the meaning.
Even though the gas did work and absorbed heat, its internal energy did not change because temperature stayed the same. \[ \boxed{\Delta U=0} \]