A carnot's engine is made to work between `200^(@)C` and `0^(@)C` first and then between `0^@C ` and `-200^(@)C`. The ratio of effeciencies of the engine in the two cases is

Options

A. `1:1.73`
B. `1.73:1`
C. `1:2`
D. `1:1`

Answer

A

Explanation

Efficiency of Carnot.s engine is given by
`eta=1-(T_(2))/(T_(1))`
where `T_(1)` is the source (higher) temperature and `T_(2)` is the sink (lower) temperature in Kelvin.
`therefor eta_(1)=1-(0+273)/(200+273)=0.423`
`eta_(2)=1-(-200+273)/(0+273)=0.732`
`thereforeetan_(1):eta_(2)=(0.423)/(0.732)=(1)/(1.73)=1:1.73`.