A Carnot engine takes `3xx10^6cal`. of heat from a reservoir at `62^@C`, and gives it to a sink at `27^@C`. The work done by the engine is

Options

A. `4.2xx10^(6)J`
B. `8.4xx10^(6)J`
C. `16.8xx10^(6)J`
D. Zero

Answer

B

Explanation

Here, `Q_(1)= 3xx10^(6)cal.`
`T_(1)=627+273= 900K`
`T_(2)= 27+273= 300K`
As `(Q_(2))/(Q_(1))= (T_(2))/(T_(1))`
`:. Q_(2)= (T_(2))/T_(1)Q_(1)=(300)/(900)xx3xx10^(6)= 10^(6)cal.`
`W= Q_(1)-Q_(2)= 3xx10^(6)-10^(6)`
`=2xx10^(6)cal.`
`=2xx10^(6)xx4.2J`
`= 8.4xx10^(6)J`