Question

A power plant burns coal at 830 K, and it exhaust to air at 288 K. If it runs at the Carnot efficiency, how much heat must it exhaust into the air to produce 230,000 J of work?

Answer 1

Correct Answer:

122000 J

Answer 2

Answer:

122241.02 J

Explanation:

Work Done = 230000 J

$T_H=\text {High Temperature Reservoir}=830\ K\\T_L=\text {Low Temperature Reservoir}=288\ K\\\text{In case of Carnot Cycle}\\\text{Efficiency}=\eta\\\eta=1-\frac{T_L}{T_H}\\\Rightarrow \eta =1-\frac{288}{830}\\\Rightarrow \eta=0.65$

$\eta=\frac{\text{Work}}{\text{Heat}}\\\Rightarrow \eta=\frac{W}{Q_H}\\\\\Rightarrow 0.65=\frac{230000}{Q_H}\\\Rightarrow Q_H=\frac{230000}{0.65}\\\Rightarrow Q_H=352214.02$

$Q_L=Q_H-W\\\Rightarrow Q_L=352214.02-230000\\\Rightarrow Q_L=122241.02\ J$

∴Heat exhausted into the air to produce 230,000 J of work is 122241.02 Joule