Question

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?

Answer 1

Answer:

(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%