# A Carnot engine operating between temperatures T1 and T2 has efficiency 1/6. When T2 is lowered by 62 K, its efficiency increases to 1/3…

Q: A Carnot engine operating between temperatures T1 and T2 has efficiency 1/6. When T2 is lowered by 62 K, its efficiency increases to 1/3. Then T1 and T2 are, respectively .

Sol: $\large \eta_1 = 1-\frac{T_2}{T_1}$

$\large \frac{1}{6} = 1-\frac{T_2}{T_1}$

$\large \frac{T_2}{T_1} = \frac{5}{6}$ … (i)

$\large \eta_2 = 1-\frac{T_2 – 62}{T_1}$

$\large \frac{1}{3} = 1-\frac{T_2 -62}{T_1}$ …(ii)

On solving Equation (i) and (ii)

T1 = 372 K and T2 = 310 K