Question

A carnot engine A operates between Tk and 540k . Another carnot's engine B operates between 200k and 600k .If both engines have same efficiency,find the temperature T.​

Answer 1

Explanation:

$\huge\bf{\mid{\overline{\underline{ANSWER:-}\mid}}}$

$\huge\bold{Given:-} \\ \\ Carnot \: \: engine (A)\: \: operates \: \: between \: \: t \: K \: to \: 540 \: K \\ \\ Carnot \: \: engine (B)\: \: operates \: \: between \: \: 200 \: K \: to \: 600 \: K \\ \\ \huge\bold{Formula:-} \\ \\ \implies \eta = 1 - \frac{T_{1}}{T_{2}} \\ \\ For \: (A) \\ \\ \implies \eta = 1 - \frac{t}{540} \\ \\ For (B) \\ \\ \implies \eta = 1 - \frac{200}{600} \\ \\ If \: \: both \: \: efficiency \: \: are \: \: same.. \\ \\ \implies \cancel{1} - \frac{t}{540} = \cancel{1} - \frac{200}{600} \\ \\ \implies \frac{t}{540} = \frac{2\cancel{00}}{6\cancel{00}} \\ \\ \implies t = \frac{540}{3} \\ \\ \huge\boxed{ \implies t = 180 \: K}$