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.
