Question

Reversible engine converts one sixth of heat absorbed at the source into work when the temperature of the sink is reduced by 82 degree Celsius the efficiency is doubled find the temperature of the source and the sink.

Answer 1

Hey dear,

◆ Answer-
Sink temperature = 328 K
Source temperature = 410 K

◆ Explanation-
# Given -
η1 = 1/5
η2 = 2×1/5 = 2/5

# Formula-
Efficiency is calculated by-
η = (T2-T1)/T2

# Solution-
Let T1 be sink temperature and T2 be source temperature.

Initially, efficiency is -
η1 = (T2-T1)/T2
1/5 = (T2-T1)/T2
T2 = 5T2-5T1
4T2 = 5T1 ...(1)

Later T2 is reduced by 82 K,
η2 = [T2-(T1-82)]/T2
2/5 = (T2-T1+82)/T2
2T2 = 5T2-5T1+410
3T2+410 = 5T1
3T2+410 = 4T2 ...from(1)
T2 = 410 K

To calculate T1,
T1 = 4T2/5
T1 = 4×410/5
T1 = 328 K

Therefore,
Sink temperature = 328 K
Source temperature = 410 K

Hope it helps...