Question

Carnot engine A has an efficiency of 0.57, and Carnot engine B has an efficiency of 0.72. Both engines utilize the same hot reservoir, which has a temperature of 615 K and delivers 1248 J of heat to each engine. Find (a), (b) the magnitude of the work produced by engine A and B respectively and (c), (d) the temperatures of the cold reservoirs that they use.

Answer 1

Answer:

710.79 Joules

898.56 Joules

264.45 K

172.2 K

Explanation:

W = Work done

Q = Heat added = 1248 J

$T_h$ = Temperature of hot reservoir = 615 K

$T_c$ = Temperature of cold reservoir

Efficiencies of engine A and B

$\eta_A$ = 0.57

$\eta_B$ = 0.72

Efficiency is given by

$\eta=\frac{W}{Q}\\\Rightarrow W=\eta Q\\\Rightarrow W=0.57\times 1248\\\Rightarrow W=711.36\ J$

Work done by engine A is 710.79 Joules

$\eta=\frac{W}{Q}\\\Rightarrow W=\eta Q\\\Rightarrow W=0.72\times 1248\\\Rightarrow W=898.56\ J$

Work done by engine B is 898.56 Joules

Efficiency

$\eta=1-\frac{T_c}{T_h}\\\Rightarrow 0.57=1-\frac{T_c}{615}\\\Rightarrow T_c=-0.43\times -615\\\Rightarrow T_c=264.45\ K$

The temperature of the cold reservoir is 264.45 K

$\eta=1-\frac{T_c}{T_h}\\\Rightarrow 0.72=1-\frac{T_c}{615}\\\Rightarrow T_c=-0.28\times -615\\\Rightarrow T_c=172.2\ K$

The temperature of the cold reservoir is 172.2 K