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 a low-temperature reservoir? (c) What is the thermal efficiency of the cycle?
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
Solution:
Given,
Temperature of high-temperature reservoir (T1) = 620 K
Energy taken in each cycle (Q1) = 550 J
Energy given to low-temperature reservoir (Q2) = 335J
Now,
Mechanical work done in each cycle = Q1 - Q2
= 550 J - 335 J
= 215 J
Let the temperature of the low reservoir be T2 then
T1/T2 = Q1/Q2
=> T2 = Q2/Q1 * T1
=> T2 = 335/550 * 620
So, T2 = 377.37 K = 378 K
Finally, let n be the efficiency of the Carnot Engine then
n = 1 - T2/T1
= 1 - 378/620
= 1 - 0.61
= 0.39
= 39%
Hence, the required mechanical work done is 215 J, the temperature of lower reservoir is 378 K and the efficiency of the Carnot engine is 39%.
