A Carnot engine takes `3xx10^6cal`. of heat from a reservoir at `627^@C`, and gives it to a sink at `27^@C`. The work done by the engine is

Options

A. `4.2 xx 10^(6)J`
B. `8.4 xx 10^(6)J`
C. `16.8 xx 10^(6)J`
D. zero

Answer

B

Explanation

`T_("source") = 627^(@)C = 627 + 273 = 900K`
`T_("sink") = 27^(@)C = 27 + 273 = 300K`
Efficiency `(eta)= 1 - (T_("sink"))/(T_("source")) = 1-(300)/(900) = 1- (1)/(3)`
`(eta) = (2)/(3) = ("Output")/("Input") = ("Work")/(Heat Input")`
`implies (2)/(3) xx "Heat Input" = "Work"`
`implies (2)/(3) xx 3xx10^(6) xx 4.2 = "Work"`
`implies "Work" = 8.4 xx 10^(6)J`