Determine the efficiency of a Carnot cycle if | vedclass

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

Question

(B) For an adiabatic process,the relationship between temperature and volume is given by $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$.Rearranging this,we

Vedclass · Accepted Answer

$1-\frac{1}{\sqrt{3}}$

Vedclass · Answer

(B) For an adiabatic process,the relationship between temperature and volume is given by $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$.Rearranging this,we get $\frac{T_2}{T_1} = \left(\frac{V_1}{V_2}\right)^{\gamma-1}$.Given that the final volume $V_2 = 3V_1$,we have $\frac{V_1}{V_2} = \frac{1}{3}$.Substituting the values $\gamma = 1.5$ and $\frac{V_1}{V_2} = \frac{1}{3}$:$\frac{T_2}{T_1} = \left(\frac{1}{3}\right)^{1.5-1} = \left(\frac{1}{3}\right)^{0.5} = \frac{1}{\sqrt{3}}$.The efficiency $\eta$ of a Carnot cycle is defined as $\eta = 1 - \frac{T_2}{T_1}$.Substituting the ratio,we get $\eta = 1 - \frac{1}{\sqrt{3}}$.

Determine the efficiency of a Carnot cycle if,in the adiabatic expansion,the volume becomes $3$ times its initial value and $\gamma = 1.5$.

Similar Questions

$A$ Carnot engine whose sink is at $300 \, K$ has an efficiency of $50 \%$. By how much should the temperature of the source be increased so that the efficiency becomes $70 \%$?

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 raised to $60\%$,then the required temperature of the sink will be: (in $K$)

$A$ Carnot engine having an efficiency of $40\%$ takes heat from a source maintained at a temperature of $500 \ K$. If the efficiency is to be increased to $60\%$ while keeping the sink temperature constant,what should be the new source temperature in $K$?

An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is ....... $^{\circ}C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module