CHEMISTRY COMMUNITY

Why does Delta U = 0 when the system is isothermal?

Technically, ΔU is only truly 0 in the case of an ideal gas. ΔU can be thought of as the gas's internal energy, comprising both potential and kinetic energy. By definition, an ideal gas does not have any interactions between particles, so potential energy is 0. That leaves kinetic energy. Temperature is a measure of the amount of kinetic energy of a substance, and because ΔT of an isothermal process is 0, that must mean that ΔU is 0. In reality, no gas is truly ideal, and therefore even though temperature is held constant in an isothermal process, there will still be some interactions between particles, leading to a change in potential energy and therefore internal energy.

When a system is isothermal, it means that the temperature is constant so only work (expansion/compression) is considered. Internal energy is not 0 because a system is isothermal; it's 0 if the system is isolated. If a system is isolated, none of its energy is transferred to the surroundings, making the internal energy constant and so the change 0. Isothermal expansion with a nonisolated system does not mean that delta U is 0.

You can try to understand this fact in one of two ways.
1) In an isothermal process temperature is constant so the delta T is equal to zero. If you recall the equation, delta U=3/2R(deltaT) if delta T is equal to zero then delta U is equal to zero.
2) If we want to keep the temperature constant for an isothermal process then we need to have the same input of heat for the work done by the system. As a result q=-w and therefore delta U is equal to zero.

Hope that helps!

Temperature is held constant, therefore the change in energy is zero (U=0). So, the heat absorbed by the gas equals the work done by the ideal gas on its surroundings.

Delta U is zero because there is no potential energy because it's an ideal gas, and no kinetic energy because delta t is zero.