
The mean kinetic energy
of a molecule of an ideal gas is given by the expression

where
is the Boltzmann constant and
is the thermodynamic temperature of the gas.
A cylinder contains
of an ideal gas. The gas is heated so that its temperature changes from
to
.
Calculate the change in internal energy of the gas molecules.
During the heating, the gas expands, doing
of work. State the first law of thermodynamics. Use the law and your answer in (a) to determine the total energy supplied to the gas.