Question

A Carnot engine has a lower operating temperature of 14.6 Celcius and efficiency of 21.2 %. By how many kelvins should the high operating temperature be increased to achieve an efficiency of 50.9 %?

Answer 1

it should be increased by 220.73K or -52.22Celsius

Step-by-step explanation:

A Carnot engine has a lower operating temperature of 14.6 Celsius and efficiency of 21.2 %. By how many kelvins should the high operating temperature be increased to achieve an efficiency of 50.9 %?

effi=
`(Th-Tc)/(Th)`

Tc=temperature of the cold reservoir in kelvin(14.6+273=287.6

Th=temperature of the hot reservoir

eff= efficiency of a carnot engine(which alway <100%)

effi=
`(Th-Tc)/(Th)`

21.2 %=1-Tc/Th

0.212=1-287.6/Th

-.788=-287.6/Th

Th=364.97K

to achieve an efficiency of 50.9%

0.509=1-Tc/Th

-0.491=-287.6/Th

Th=585.74K

taking the difference between the two high temperatures

585.74K-364.97K

220.73K

it should be increased by 220.73K