Question

Calculate the work performed by an ideal Carnot engine as a cold brick warms from 150 K to the temperature of the environment, which is 300 K. (Use 300 K as the temperature of the hot reservoir of the engine). The heat capacity of the brick is C = 1 kJ/K.

Answer 1

Answer:

57.94415 kJ

Explanation:

$T_h$ = Environment temperature = 300 K

$T_c$ = Brick temperature = 150 K

C = Specific heat of brick = 1 kJ/K

Work done is given by

$W=\int_{T_c}^{T_h}C(1-\dfrac{T_h}{T})\\\Rightarrow W=C(T_h-T_c)-T_hCln\dfrac{T_h}{T_c}\\\Rightarrow W=1(300-150)-300\times 1ln\dfrac{300}{150}\\\Rightarrow W=-57.94415\ kJ$

The work performed is 57.94415 kJ