The efficiency of carnot's heat engine is 0.5 when the temperature of the source is `T_(1)` and that of sink is `T_(2)` .The efficiency of another carnot's heat engine is also 0.5.the temperature of source and sink of the second engine are respectively

Options

A. `2T_(1),2T_(2)`
B. `2T_(1),(T_(2))/(2)`
C. `T_(1)+5,T_(2)-5`
D. `T_(1)+10,T_(2)-10`

Answer

A

Explanation

Efficiency or carot's heat engine
`eta=1-(t_(2))/(T_(1))`
For first carnot's heat engine , 0.5 =1-`(T_(2))/(T_(1))`
for second heat engine, 0.5 =1-`(T_(2))/(T_(1))`
Efficiency remains the same when both `T_(1)` and `T_(2)` are increase by same factor
Therefore the temperature of soucre and sink of second sengine are
`T_(1)=2T_(1), T_(2)=2T_(2)`