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

To solve this problem, apply the concepts related to the calculation of the work performed according to the temperature change (in an ideal Carnot cycle), for which you have to:

$W = \int\limit_{T_c}^{T_H} C (1-\frac{T_H}{T})$

Where,

C = Heat capacity of the Brick

$T_C$= Cold Temperature

$T_H$ = Hot Temperature

Integrating,

$W = C (T_H-T_C)- T_H C ln (\frac{T_H}{T_C})$

Our values are given as

$T_H= 300K$

$T_C = 150K$

Replacing,

$W = (1) (300-150)-300(1)ln(2)$

$W = 150-300ln2$

$W = -57.94kJ \approx 58kJ$

Therefore the work perfomed by this ideal carnot engine is 58kJ