Question

4. The nighttime temperature on Mars during its Summertime can be as low as -70.0°C. A. What would be the Carnot Efficiency of an engine whose Hot Reservoir is operated at 250.°C (please provide your answer as a percentage)? How much energy must be input to this engine for it to do 500. MJ of work (please provide your answer 500.kW h)? B.

Answer 1

Given,

Temperature of cold reservoir, T_c = -70 ^{$^{\circ}$} C = (273.15 + (-70))

                                                       = 203.15 K

Temperature of hot reservoir, T_h = 250 ^{$^{\circ}$} C = (273.15 +250)

                                                       = 523.15 K

Now,

efficiency, $\eta$ = (1 - (T_c/T_h))*100

                      = (1 - (203.15 / 523.15))*100

                      = (1 - 0.39)*100 = 0.61*100

                       = 61%

Now,

Work done, W = 500 MJ

Let heat provided be Q_H

Now,

efficiency, $\eta$ = W / Q_H

=> 0.61 = 500 * 10⁶ / Q_H

=> Q_H = (500 * 10⁶) / 0.61

            = 819.67 * 10⁶

1 kWh = 3.6 * 10⁶ J

thus,

Q_H = (819.67 * 10⁶ / 3.6 * 10⁶ ) kWh

     = 227.69 kWh