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

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

Question

(D) Given,temperature of sink,$T_2 = 500\,K$.Efficiency,$\eta_1 = 50\% = 0.5$.The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1

Vedclass · Accepted Answer

$400$

Vedclass · Answer

(D) Given,temperature of sink,$T_2 = 500\,K$.Efficiency,$\eta_1 = 50\% = 0.5$.The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$.Substituting the values: $0.5 = 1 - \frac{500}{T_1} \implies \frac{500}{T_1} = 0.5 \implies T_1 = 1000\,K$.Now,the temperature of the source $T_1$ is kept constant at $1000\,K$.New efficiency,$\eta_2 = 60\% = 0.6$.Let the new temperature of the sink be $T_2'$.Using the formula: $\eta_2 = 1 - \frac{T_2'}{T_1}$.$0.6 = 1 - \frac{T_2'}{1000}$.$\frac{T_2'}{1000} = 1 - 0.6 = 0.4$.$T_2' = 0.4 	imes 1000 = 400\,K$.

The efficiency of a Carnot engine is $50\%$ and the temperature of the sink is $500\,K$. If the temperature of the source is kept constant and its efficiency is to be raised to $60\%$,then the required temperature of the sink will be ........... $K$.

Similar Questions

$A$ Carnot heat engine has an efficiency of $20 \%$. The energy is supplied to the engine at the rate of $2 \text{ kW}$. The output power of the engine is (in $\text{ W}$)

$A$ Carnot engine with efficiency $50\%$ takes heat from a source at $600\text{ K}$. To increase the efficiency by $20\%$, keeping the temperature of the sink the same, the new temperature of the source will be: (in $\text{ K}$)

$A$ diatomic ideal gas is used in a Carnot engine as a working substance. If during the adiabatic expansion part of the cycle,the volume of the gas increases from $V$ to $32V$,the efficiency of the engine is:

$A$ Carnot engine, whose efficiency is $40\%$, takes heat from a source maintained at temperature $600\text{ K}$. To have an efficiency of $60\%$, the intake temperature for the same exhaust temperature should be: (in $\text{ K}$)

$A$ Carnot engine of efficiency $40 \%$ takes heat from a source maintained at a temperature of $500 \ K$. It is desired to have an engine of efficiency $60 \%$. Then,the source temperature for the same sink temperature must be (in $K$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module