Question

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)

Hint:

For isothermal expansion of an ideal gas, remember that the internal energy change (∆U) is always zero, as it depends only on the temperature, which remains constant.

Answer 1

Correct Answer: 0

In the given scenario, we are dealing with the isothermal expansion of an ideal gas into a vacuum. For an isothermal process, the temperature remains constant. According to the first law of thermodynamics, the change in internal energy (ΔU) for a process can be expressed as:

ΔU = Q - W

where Q is the heat exchanged, and W is the work done by the system. However, in an isothermal expansion of an ideal gas into a vacuum (also known as free expansion), the following considerations apply:

1. Since the process is isothermal, the internal energy of an ideal gas (which depends only on temperature) does not change. This means ΔU = 0 J because temperature is constant.
2. In a free expansion into a vacuum, no work is performed (\( W = 0 \) J) because there is no external pressure resisting the expansion.
3. No heat exchange with the surroundings occurs (\( Q = 0 \) J) since it’s an isolated process.

Thus, applying these conditions to the first law of thermodynamics, we confirm:

ΔU = Q - W = 0 - 0 = 0

Therefore, the change in internal energy for this isothermal expansion into a vacuum is 0 J, and it falls within the specified range of 0 to 0.