Q$1.$

$($a$)$ When a refrigerator functions, heat is removed from it$.$ State whether with respect to the refrigerator this heat is positive or negative and justify your answer.

$($b$)$ When swimming, an athlete gives off ${10}^{5}J$ of heat and does $2{10}^{5}J$ of work. What is the change in the internal energy of the athlete and how will this change affect his temperature?

$(2$ marks$)$

$($c$)$ When compressing a sample of gas, $50$ J of work is done. The gas then cools down by releasing $15J$ of heat energy into its surroundings.

i$)$ What is the change in the internal energy of the gas?

ii$)$ Is this process isothermal, adiabatic or none of those? Explain your answer.

Q$2.$

$(2$ marks$)$

$($a$)$ A Carnot engine operates between a hot and cold temperature.

$($i$)$ If the efficiency of the engine is $30\%$ and the cold reservoir temperature is $300$ K $,$ determine the temperature of the hot reservoir.

$($ii$)$ Calculate how much work is produced by the engine if it is provided with $5000$ J of heat.

$(1$ mark$)$

$($iii$)$ Determine how much heat is discarded to the cold reservoir as this work

$(1$ mark$)$

$($iv$)$ Is it possible to increase the efficiency of this engine without changing the hot and cold reservoir temperatures?