Question

The internal energy U of an ideal gas depends only on its temperature T, not on its pressure or volume.

Answer 1

Hint: You can use the relation internal energy (U) depends on temperature (T) and the number of moles (n) i.e. $U = {K_{trans}} = \dfrac{3}{2}nKT$ and also the relation \[T = \dfrac{1}{{nR}}PV\]and find the reason for the statement mentioned in the question.

Complete Step-by-Step solution:
The given statement is true because
We know that the only contribution to the internal energy comes from the translational kinetic energy (for monatomic ideal gas) according to.
$U = {K_{trans}} = \dfrac{3}{2}nKT$
So, obviously, the internal energy (U) depends only on the temperature (T) and the number of moles (n) of the gas. But if someone did work on the gas leading to an increase in pressure and decrease in volume and according to \[T = \dfrac{1}{{nR}}PV\] if we increase the pressure the volume will decrease and the temperature will remain constant.

Note: From the fundamental equations for internal energy and enthalpy, the volume dependence of internal energy and the pressure dependence of enthalpy for ideal gases are derived. By applying property relations, it is proved that the internal energy and enthalpy of ideal gases do not depend on volume and pressure, respectively.