Carnot engine takes one thousand kilo calories of heat from a reseervoir at `827^@C` and exhausts it to a sink at `27^@C`. How, much work does it perform? What is the efficiency of the engine?

Options

A. `2.7 xx10^(5)` cal, 70.70%
B. `2,72 xx 10^(5)`, cal 72.72%
C. `2.70 xx 10^(5)` cal, 80.70%
D. `3.70 xx 10^(5)` cal, 70.70%

Answer

B

Explanation

Given, `Q= 10^(6)` cal
`T_(1)= 827^(@)C = (827+273)= 1100K`
`T_(2)= 27^(@)C= (27+273)= 300K`
As, `(Q_(1))/(T_(1))= (Q_(2))/(T_(2))`
`therefore Q_(2)= (T_(2))/(T_(1)) Q_(1)= (300)/(1100) xx 10^(6)`
`=2.72 xx 10^(5)` cal
Efficiency of the engine,
`eta = (1- (T_(2))/(T_(1))) xx 100`
`eta = (1- (300)/(1100)) xx 100`
`=72.72%`