When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre, the change in internal energy is ____________ J. (Nearest integer)

Solution

Chemistry ma’am · 4 steps

Isothermal ideal gas means fixed temperature, so the internal energy has no reason to change.

1. U depends on T. For an ideal gas there are no forces between molecules, so U depends only on temperature. Volume and pressure do not enter it.
2. Isothermal expansion. The temperature stays fixed, so Δ T = 0 and therefore Δ U = nC_VΔ T = 0.
3. Check with first law. Expansion into vacuum is free expansion: pₑₓₜ = 0, so w = -pₑₓₜΔ V = 0. With Δ U = 0, the first law Δ U = q + w gives q = 0 too.

   Δ U = q + w = 0 + 0 = 0

4. So. The volumes 2 L and 6 L do not matter here. The change in internal energy is 0 J.

The idea to keep. For an ideal gas, Δ U depends only on Δ T. Any isothermal process gives Δ U = 0, and free expansion into vacuum also gives w = 0 and q = 0.

Answer from the NTA final answer key. Solution by PrepWiser.