The p-V diagram of a Carnot's engine is shown | vedclass

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

Question

(C) The efficiency $\eta$ of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1} = \frac{W}{Q_1}$.From the $p-V$ diagram,the process $AB$ is isoth

Vedclass · Accepted Answer

$3000$

Vedclass · Answer

(C) The efficiency $\eta$ of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1} = \frac{W}{Q_1}$.From the $p-V$ diagram,the process $AB$ is isothermal expansion at $T_1$ and $CD$ is isothermal compression at $T_2$.For an isothermal process,$pV = 	ext{constant}$.At point $A$: $p_A = 1600 \ kPa$,$V_A = 2.5 \ cm^3$. So,$p_A V_A = 1600 	imes 2.5 = 4000$.At point $C$: $p_C = 400 \ kPa$,$V_C = 6.25 \ cm^3$. So,$p_C V_C = 400 	imes 6.25 = 2500$.Since $pV = \mu RT$,we have $\frac{T_2}{T_1} = \frac{p_C V_C}{p_A V_A} = \frac{2500}{4000} = \frac{5}{8} = 0.625$.The efficiency is $\eta = 1 - 0.625 = 0.375$.Given heat supplied $Q_1 = 8000 \ J$.Work done $W = \eta 	imes Q_1 = 0.375 	imes 8000 = 3000 \ J$.

Similar Questions

$A$ Carnot engine having efficiency $60 \%$ receives heat from a source at a temperature $600 \text{ K}$. For the same sink temperature, to increase its efficiency to $80 \%$, the temperature of the source is (in $\text{ K}$)

$A$ Carnot engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is lowered by $57 \ K$,its efficiency becomes $\frac{1}{3}$. The temperature of the source is: (in $K$)

$A$ Carnot engine operates between a source and a sink. The efficiency of the engine is $40 \%$ and the temperature of the sink is $27^{\circ} C$. If the efficiency is to be increased to $50 \%$,then the temperature of the source must be increased by: (in $K$)

$A$ 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 $K$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module