A carnot engine whose efficiency is 40 %, receives heat at 500 K. If the efficiency is tobe 50 %, the source temperature for the same exhaust temperature is

Question

A carnot engine whose efficiency is 40 %, receives heat at 500 K. If the efficiency is tobe 50 %, the source temperature for the same exhaust temperature is (A) 900 K (B) 600 K (C) 700 K (D) 800 K

Tardigrade Admin · Accepted Answer

We know that, efficiency of a Carnot engine is given by

η = (1 - \frac{T _{2}}{T _{1}})

Given,

η_{1} = 0.4

and

T_{1} = 500 K

(temperature of source)
So,

0.4 = 1 - \frac{T _{2}}{500}

\Rightarrow \frac{T _{2}}{500} = 1 - 0.4 = 0.6

\Rightarrow T_{2} = 0.6 \times 500 = 300 K

(temperature of sink)
Now, in the second gas,

η = 0.5

and

T_{2} = 300 K

∴ 0.5 = (1 - \frac{300}{T _{1}})

\Rightarrow \frac{300}{T _{1}} = 1 - 0.5 = 0.5

\Rightarrow T_{1} = \frac{300}{0.5} = 600 K

Q. A carnot engine whose efficiency is $40%$ , receives heat at $500 K$ . If the efficiency is tobe $50%$ , the source temperature for the same exhaust temperature is

$900 K$

$600 K$

$700 K$

$800 K$

Q. A carnot engine whose efficiency is 40%, receives heat at 500K. If the efficiency is tobe 50%, the source temperature for the same exhaust temperature is

900K

600K

700K

800K

Q. A carnot engine whose efficiency is $40%$ , receives heat at $500 K$ . If the efficiency is tobe $50%$ , the source temperature for the same exhaust temperature is

$900 K$

$600 K$

$700 K$

$800 K$