A Carnot engine whose high-temperature reservoir is at 620 k takes in 550 J of heat at this temperature in each cycle and gives up 335 J to the low temperature reservoir.

(a) How much mechanical work does the engine perform during each cycle?

(b) What is the temperature of the low-pressure reservoir?

(c) What is the thermal efficiency of the cycle?

(a) W=217 J

(b) Tc=378K

(c) e=0.39=39%

Explanation:

For part (a)

We to calculate the mechanical work W the engine does. By knowing QC and QH can obtain the work using equation

W = IQHI - IQcl ... eq (1)

Put given values for QH and QC into equation (1) to get

the mechanical work of the engine

W = 550 - 335

W=217 J

For part (b)

We want to determine the temperature of low temperature reservoir which means Tc

IQc|/|Qh| = TC/TH

for Tc

Tc = (IQc|/|Qh|) * TH

Now we can put values

Tc = 620K (335 / 550.1)

Tc=378K

For part (c)

Here we want to find the thermal efficiency (e) of the cycle

e=1-TC/TH

e=1 - (378/620)

e=0.39=39%