A Carnot engine operating between temperature | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$.Given $\eta_1 = \frac{1}{6}$,we have $1 - \frac{T_2}{T_1} = \frac{1}{6}

Vedclass · Accepted Answer

$372\, K$ and $310\, K$

Vedclass · Answer

(C) The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$.Given $\eta_1 = \frac{1}{6}$,we have $1 - \frac{T_2}{T_1} = \frac{1}{6}$,which implies $\frac{T_2}{T_1} = \frac{5}{6}$ or $T_2 = \frac{5}{6}T_1$.When $T_2$ is lowered by $62\, K$,the new temperature is $T_2' = T_2 - 62$. The new efficiency is $\eta_2 = \frac{1}{3}$.So,$1 - \frac{T_2 - 62}{T_1} = \frac{1}{3}$,which implies $\frac{T_2 - 62}{T_1} = \frac{2}{3}$.Substituting $T_2 = \frac{5}{6}T_1$ into the second equation: $\frac{\frac{5}{6}T_1 - 62}{T_1} = \frac{2}{3}$.$\frac{5}{6} - \frac{62}{T_1} = \frac{2}{3}$.$\frac{62}{T_1} = \frac{5}{6} - \frac{2}{3} = \frac{5-4}{6} = \frac{1}{6}$.$T_1 = 62 	imes 6 = 372\, K$.Now,$T_2 = \frac{5}{6} 	imes 372 = 5 	imes 62 = 310\, K$.Thus,$T_1 = 372\, K$ and $T_2 = 310\, K$.

$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has an efficiency of $\frac{1}{6}$. When $T_2$ is lowered by $62\, K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are,respectively:

Similar Questions

When ${}_{92}U^{238}$ changes into ${}_{82}Pb^{206}$,the number of $\alpha$ and $\beta^-$ particles emitted are:

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction,when the angle of inclination of the plane is $60^{\circ}$,is

If $\sin ^{-1}\left(\frac{3}{x}\right)+\sin ^{-1}\left(\frac{4}{x}\right)=\frac{\pi}{2}$,then $x$ is equal to

$A$ capacitor is charged by using a battery,which is then disconnected. $A$ dielectric slab is then inserted between the plates. What is the result?

The conjugate acid of $NH_2^-$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module