The efficiency of a Carnot engine is 50 % whe | vedclass

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

Question

(B) The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$,where $T_1$ is the source temperature and $T_2$ is the sink temperature

Vedclass · Accepted Answer

$400$

Vedclass · Answer

(B) The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$,where $T_1$ is the source temperature and $T_2$ is the sink temperature.Given $\eta = 0.5$ and $T_2 = 500 \ K$,we have $0.5 = 1 - \frac{500}{T_1}$,which gives $\frac{500}{T_1} = 0.5$,so $T_1 = 1000 \ K$.Now,keeping the source temperature $T_1 = 1000 \ K$ constant,we want to achieve an efficiency $\eta' = 0.6$ by changing the sink temperature to $T_2'$.Using the formula $\eta' = 1 - \frac{T_2'}{T_1}$,we get $0.6 = 1 - \frac{T_2'}{1000}$.Rearranging the terms,$\frac{T_2'}{1000} = 1 - 0.6 = 0.4$.Therefore,$T_2' = 0.4 	imes 1000 = 400 \ K$.

The efficiency of a Carnot engine is $50 \%$ when the temperature of the sink is $500 \ K$. If the efficiency of the Carnot engine is to be increased to $60 \%$,what should be the temperature of the sink,keeping the temperature of the source constant (in $K$)?

Similar Questions

The temperature of the sink of a Carnot engine is $250 \ K$. In order to increase the efficiency of the Carnot engine from $25 \%$ to $50 \%$,the temperature of the sink should be increased by

$A$ reversible engine has an efficiency of $\frac{1}{4}$. If the temperature of the sink is reduced by $58^{\circ}C$,its efficiency becomes double. Calculate the temperature of the sink in $^{\circ}C$.

In a Carnot engine,the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink. The efficiency of the engine is (in $\%$)

$Assertion :$ The Carnot cycle is useful in understanding the performance of heat engines.
$Reason :$ The Carnot cycle provides a way of determining the maximum possible efficiency achievable with reservoirs of given temperatures.

Who first proposed (invented) the Carnot engine?

Vedclass Test Series

Exam Paper Generator

Online Exam Module