A diatomic gas is used in a Carnot heat engin | 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 $\eta = 1 - \frac{T_2}{T_1}$.Given $\eta = 80\% = 0.8$,we have $0.8 = 1 - \frac{T_2}{T_1}$,wh

Vedclass · Accepted Answer

$(\frac{1}{5})^{\frac{5}{2}}$

Vedclass · Answer

(C) The efficiency $\eta$ of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$.Given $\eta = 80\% = 0.8$,we have $0.8 = 1 - \frac{T_2}{T_1}$,which implies $\frac{T_2}{T_1} = 0.2 = \frac{1}{5}$.For an adiabatic process,the relation between temperature and volume is $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$.Rearranging this,we get $\frac{T_1}{T_2} = (\frac{V_2}{V_1})^{\gamma-1}$.Since $\frac{T_1}{T_2} = 5$,we have $5 = (\frac{V_2}{V_1})^{\gamma-1}$.For a diatomic gas,the adiabatic index $\gamma = 1.4 = \frac{7}{5}$,so $\gamma - 1 = \frac{2}{5}$.Thus,$5 = (\frac{V_2}{V_1})^{2/5}$.Taking the power of $5/2$ on both sides,we get $(\frac{V_2}{V_1}) = 5^{5/2}$.Therefore,the ratio of initial volume to final volume is $\frac{V_1}{V_2} = (\frac{1}{5})^{5/2}$.

$A$ diatomic gas is used in a Carnot heat engine. If the efficiency of the given Carnot heat engine is $80\%$,then find the ratio of the initial volume to the final volume of the gas during adiabatic expansion.

Similar Questions

$A$ scientist claims that their heat engine has an efficiency of $26\%$ when operating between a source temperature of $127^{\circ}C$ and a sink temperature of $27^{\circ}C$. This implies that:

$A$ 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 $\text{ K}$)

What is the efficiency of an ideal gas?

$A$ Carnot engine has an efficiency of $50 \%$. If the temperature of the sink is reduced by $40 \, K$,its efficiency increases by $30 \%$. The temperature of the source will be $.... \, K$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module