An inventor claims to have developed an engine that during a certain time interval takes in 110 MJ of heat at 415 K, rejects 50 MJ of heat at 212 K while manages to do 16.7 kWh of work. Do you agree with the inventor.s claim ?

Explanation

The claimed efficiency
`eta_(C ) = (W)/(Q_(H))=(16.7kWh)/(110MJ)`
But as `1kWh=10^(3)xx(J//s) xx (60 xx 60s) = 3.6MJ`
So `eta_(c )=(16.7xx3.6)/(110) = 0.55 = 55% …………(1) `
while maximum possible theoretical efficiency,
`eta_("max")=1-(T_(L))/(T_(H))=(T_(H)-T_(L))/(T_(H)) = (415-212)/(415)`
`=0.49=49%" "......(2)`
From Eqns. (1) and (2) it is clear that claimed efficiency is greater than maximum possible theoretical efficiency, so inventor.s claim does not appear to be correct.