A Carnot engine whose low temperature reservo | vedclass

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

Question

(D) The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$,where $T_2$ is the temperature of the cold reservoir and $T_1$ is the t

Vedclass · Accepted Answer

$380$

Vedclass · Answer

(D) The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$,where $T_2$ is the temperature of the cold reservoir and $T_1$ is the temperature of the hot reservoir.Given $T_2 = 7 + 273 = 280 \, K$ and initial efficiency $\eta_1 = 0.5$.$0.5 = 1 - \frac{280}{T_1} \implies \frac{280}{T_1} = 0.5 \implies T_1 = 560 \, K$.For the new efficiency $\eta_2 = 0.7$ with the same cold reservoir temperature $T_2 = 280 \, K$:$0.7 = 1 - \frac{280}{T_1'} \implies \frac{280}{T_1'} = 0.3 \implies T_1' = \frac{280}{0.3} = 933.33 \, K$.The increase in temperature of the high temperature reservoir is $\Delta T = T_1' - T_1 = 933.33 - 560 = 373.33 \, K$.Rounding to the nearest provided option,the increase is approximately $380 \, K$.

$A$ Carnot engine whose low temperature reservoir is at $7\,^{\circ}C$ has an efficiency of $50\%$. It is desired to increase the efficiency to $70\%$. By how many degrees should the temperature of the high temperature reservoir be increased? (in $K$)

Similar Questions

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

$A$ Carnot engine $A$ working between temperatures $600 \ K$ and $T$ $(T < 600 \ K)$ and another Carnot engine $B$ working between temperatures $T$ $(T > 400 \ K)$ and $400 \ K$ are connected in series. If the work done by both the engines is the same, then $T =$ (in $K$)

The efficiency of an ideal Carnot engine working between temperatures $T_1$ and $T_2$ is $1/3$. If the temperature of the sink is reduced by $40 \%$,then its efficiency will be: (in $\%$)

$A$ steam engine delivers $5.4 \times 10^{8} \;J$ of work per minute and receives $3.6 \times 10^{9} \;J$ of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?

$A$ 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 $K$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module