Question

What is the internal energy for an isothermal process?

Answer 1

Hint: Isothermal process is defined as the process in which the temperature of the system remains fixed throughout the whole process. We are going to briefly explain it on the basis of the First Law of Thermodynamics to find the answer.

Complete step by step solution:
A process in which the temperature of the system is kept fixed throughout is called an isothermal process also known as constant-temperature process. For a process to be isothermal, any heat flow into or out of the system must occur very slowly so that it always maintains thermal equilibrium.
In general, for an isothermal process none of the quantities $\mathrm{\Delta }$U, W or Q is zero, but in some special cases the internal energy of a system depends only on its temperature, not on its pressure or volume. The most common system following this special case is an ideal gas. For ideal gas if temperature is constant, the internal energy is also constant, $\mathrm{\Delta }$U$=0$ and hence the first law of thermodynamics then implies that heat supplied to the gas equals the work done by the gas, Q$=$W.
For an isothermal process, the ideal gas equation, PV$=$$\mu$RT gives PV$=$constant, which is just Boyle's law.
So, the internal energy for an isothermal process is considered to be $0$.

Note:
It must be noted that heat actually flows in an isothermal process generally, which is very slow. But for ideal gas, no exchange of heat takes place. Work is done in case of an isothermal process which depends on the final and the initial volume.