Question $1-$ Thermodynamics

$[$Total $25$ Marks$]$

a$)$ An electric heater with power rating of $0\mathrm{.}5$ kW is placed at the centre of a closed room. The initial average temperature of the room is $15C($state $1).$ The electric heater is switched on for $2$ hours $($take state $2$ as the state after three hours$).$ The total volume of the room is $31m^3.$ Heat loss to the surroundings during the two hours was $3000$ kJ $.$ Consider that the density of air to be constnt at $1\mathrm{.}2k\frac{g}{m^3}$ and the specific heat capacity of air to be constant at $c=0\mathrm{.}7k\frac{J}{k}g*K.$

i$.$ Determine the net heat gain or loss by the air in the room during process $1-2.$

$[5$ marks$]$

ii$.$ Determine the temperature of the room at state $2.$

$[5$ marks$]$

b$)0\mathrm{.}12$ kg of carbon dioxide is contained in a cylinder piston arrangement as shown in Figure Q$1.$ The gas has initial pressure of $150$ kPa and temperature of $20C.$ Carbon dioxide is compressed isothermally until the pressure reaches $250$ kPa $.($for carbon dioxide, $R=0\mathrm{.}1889k\frac{J}{k}g*K).$

i$.$ Sketch process $1-2$ on a P$-$v diagram showing points $1$ and $2$ and the path of the process with an arrow showing the process direction.

$[5$ marks$]$

ii$.$ Calculate the volume of carbon dioxide in the cylinder at states $1$ and $2.$

$[5$ marks$]$

iii. Calculage the work done by the piston on the surroundings during process $12.$

$[5$ marks$]$