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

710.79 Joules

898.56 Joules

264.45 K

172.2 K

Step-by-step 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=(W)/(Q)\\\Rightarrow W=\eta Q\\\Rightarrow W=0.57* 1248\\\Rightarrow W=711.36\ J`

Work done by engine A is 710.79 Joules

`\eta=(W)/(Q)\\\Rightarrow W=\eta Q\\\Rightarrow W=0.72* 1248\\\Rightarrow W=898.56\ J`

Work done by engine B is 898.56 Joules

Efficiency

`\eta=1-(T_c)/(T_h)\\\Rightarrow 0.57=1-(T_c)/(615)\\\Rightarrow T_c=-0.43* -615\\\Rightarrow T_c=264.45\ K`

The temperature of the cold reservoir is 264.45 K

`\eta=1-(T_c)/(T_h)\\\Rightarrow 0.72=1-(T_c)/(615)\\\Rightarrow T_c=-0.28* -615\\\Rightarrow T_c=172.2\ K`

The temperature of the cold reservoir is 172.2 K