A carnot engine has the same efficiency between 800 K and 500 K and x K to 400 K. What is the value of x ?

Options

A. 900 K
B. 750 K
C. 640 K
D. 550 K

Answer

C

Explanation

In the first case, `eta_(1)=(T_(1)-T_(2))/T_(1)=(800-500)/800=3/8`
In the second case, the source temperature is x and sink temperature = 400K and `eta_(1)=eta_(2)`
`thereforeeta_(2)=3/8=(x-400)/x=1-400/x`
`therefore400/x=1-3/8=5/8`
`therefore5x=3200" "thereforex=640K`