a$)$ A piston$-$cylinder device contains $0\mathrm{.}4m^3$ of air at $350$ kPa $.$ Air is heated isobarically till its volume doubles.

i$.$ Determine the work in kJ and $3$s$.$f$.$

$[1$ marks$]$

ii$.$ Use units and show how you validated your result.

$[2$ marks$]$

b$)$ A scientist claims to have developed a refrigerator that produces a $350$ kW cooling effect for a $3C$ cooling zone while only using $70$ kW of power and removing the heat to the surroundings at $25C.$

i$.$ Justify the validity of this claim with your calculation.

$[2$ marks$]$

c$)$ A standing person is modelled as a $35$ cm diameter, $170$ cm long vertical cylinder. Both top and bottom surfaces are insulated. The side surface at an average temperature of $36C.$ Convection heat transfer coefficient is $16\frac{W}{m^2}C.$ The emissivity of his clothes is $0\mathrm{.}92.$ The Stefan$-$Boltzmann constant is $5\mathrm{.}670{10}^{-8}\frac{W}{m^2}*K^4.$ Determine:

i$.$ the rate of total heat loss to the environment at $20C.$

$[2$ marks$]$

d$)2\mathrm{.}5$ kg of water at $20C$ is to be heated to $95C$ in a $3$ kW kettle. The specific heat of water is $4\mathrm{.}18k\frac{J}{k}gK.$ The kettle is $1$ kg and has an average specific heat of $0\mathrm{.}8k\frac{J}{k}gK.$ Consider heat losses negligible.

i$.$ Find how long it will take for the water to be heated.

$[3$ marks$]$

ii$.$ If the same amount of water takes $10$ minutes to heat$-$up$,$ calculate the heat losses in kJ$.$

$[2$ marks$]$