Question

1. As the hero or heroine of a TV show, you must rescue a football player who has been frozen solid by the Evil Conspiracy a) He's being held in a freezer at a temperature of 0.00°C which has a coefficient of per- formance equal to 0.600 times the ideal K. The temperature of the room is 19.0°C If the freezer gains heat from the room at a rate of 48.0W, how much power does the freezer need? b) You thaw the football player in jig time by inventing a Jig Thaw Chamber, which is perfectly insulated and contains an electric heater. Approximate him as a block of ice of mass 145 kg. How much heat do you have to add to raise his temperature to 37.0 °C? e 1.60 x 10-19 C o 8.85 x1012 C2 IN m2 For water, L 333 x 103 J/kg, Ly - 2260 x 103 J/kg, Cice 2.11 x103 Jkg oC, Cliquid 4.19 x 103 J/kg.°C, ki0.590 W m.°C.

Answer 1

1 (a) The ideal coefficient of performance is given by,

$COP = \frac{T_c}{T_h - T_c}$

The cold reservoir is 273 K and the hot reservoir is at 19 degree celsius which is 292 K. Substituting values we get,

$\Rightarrow K = \frac{273}{292-273} = 14.37$

We also know that the coefficient of performance is,

Here Q is the heat removed and W is the work done. It is given that the freezer gains 48 J/s from the room, Hence the same amount of heat has to be removed so that the freezer can be maintained at constant temperature. Therefore we can find the amount of work done by substituting the values into the above equation.

$\Rightarrow 0.6K = \frac{48}{W} \Rightarrow (0.6)(14.37) = \frac{48}{W} \Rightarrow W = 5.57 \, J/s$

Hence the power required by the freezer is 5.57 W.

(b) For reaching temperature we have to melt the ice at 0 degrees to form water at 0 degrees and then increase the temperature of water to 37 degrees. Therefore the total amount of heat required is,

Substituting values we get, the amount of heat required as

Η (145)(333000 + (4190)(37)) = 7.08 × 10' J