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

$A$ Carnot engine converts $1/6$th of the heat into work. When the temperature of the sink is reduced by $62 \ K$,the efficiency of the engine is doubled. Calculate the temperatures of the source and the sink.

The following figure shows a Carnot engine that works between temperatures $T_1=400 \text{ K}$ and $T_2=200 \text{ K}$ and drives a Carnot refrigerator that works between temperatures $T_3=350 \text{ K}$ and $T_4=250 \text{ K}$. The quantity $\frac{Q_3}{Q_1}$ will be

$A$ Carnot engine whose efficiency is $40 \%$, receives heat at $500 \ K$. If the efficiency is to be $50 \%$, the source temperature for the same exhaust temperature is (in $K$)

$A$ Carnot engine whose sink is at $300\, K$ has an efficiency of $40\%.$ By how much should the temperature of the source be increased so as to increase its efficiency by $50\%$ of its original efficiency? (in $K$)

In a Carnot engine,as the gas gives heat energy to the sink,the temperature of the sink

Vedclass Test Series

Exam Paper Generator

Online Exam Module