b$.$ A gas inside a piston$-$cylinder device at temperature of $298$ K with no moving boundaries is placed in a boiling water. The temperature of the gas rises to $373$ K and $8368$ J of heat was transferred to the gas. Then, as the piston rises the gas does $0\mathrm{.}024$ kcal of work at temperature of $373$ K$.$

$1.$ Draw a sketch of the process and specify the system boundary?

$3$ marks

L Write the energy balance equation needed for the two stages of the process and give reasons for assumptions made.

Calculate the unknown energy terms in joules.

$6$ marks

$23$