$1-$ Write the general energy balace for open unsteady$-$state systems and express mathematically. Using this expression, derive energy balances for;

$(20$ p$.)$

a$)$ Closed systems,

b$)$ Open systems in steady state,

c$)$ For a throttling valve

$2-$ Consider a steam power plant operating on the simple ideal Rankine cycle. Steam enters the turbine at $2$MPa and $360C$ and is condensed in the condenser at a pressure of $0\mathrm{.}8$MPa.

$(40$ p$.)$

a$)$ Determine the net work done.

b$)$ Determine the thermal efficiency of this cycle.

c$)$ If the turbine and pump operate at $0\mathrm{.}80$ isentropic efficiency, calculate the net work and thermal efficiency.

The pump work will not be neglected.

$3-$ A refrigerator uses refrigerant$-134$a as the working fluid and operates on an ideal vapor$-$compression refrigeration cycle between $0\mathrm{.}14$ and $0\mathrm{.}8$MPa. If the mass flow rate of the refrigerant is $0\mathrm{.}05k\frac{g}{s},$ determine

$(40$ p$.)$

a$)$ The rate of heat removal from the refrigerated space and the power input to the compressor, b$)$ The rate of heat rejection to the environment, and c$)$ The COP of the refrigerator.