Question

In which of the following thermodynamic process, the internal energy of system remains constant

• A. Isobaric
• B. Isochoric
• C. Adiabatic
• D. Isothermal

Hint:

Look at the prefix: "Iso" means same, "thermal" means temperature. Same temperature = same internal energy for an ideal gas!

Answer 1

The Correct Option is D

Step 1: What changes internal energy?
For an ideal gas, internal energy depends only on temperature: $dU = nC_{v}\,dT$. So if temperature is fixed, internal energy is fixed.

Step 2: What we are looking for.
We need the process where $dU = 0$, which means $dT = 0$ (constant temperature).

Step 3: Check isobaric.
Constant pressure, but temperature can change, so $U$ changes. Not this one.

Step 4: Check isochoric.
Constant volume, but temperature still changes, so $U$ changes. Not this one.

Step 5: Check adiabatic.
No heat is exchanged, but the gas expands or compresses and temperature changes. So $U$ changes.

Step 6: Check isothermal.
Here temperature is held constant, so $dT = 0$ and $dU = 0$. This is the right one, option 4.
\[ \boxed{\text{Isothermal process}} \]