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

An engine is supposed to operate between two reservoirs at temperatures $727^oC$ and $227^oC$. The maximum possible efficiency of such an engine is:

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

Consider a Carnot cycle operating between $T_1 = 500\, K$ and $T_2 = 300\, K$ producing $1\, kJ$ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.

$A$ Carnot engine works first between $200^{\circ} C$ and $0^{\circ} C$ and then between $0^{\circ} C$ and $-200^{\circ} C$. The ratio of its efficiency in the two cases is

Which type of process is performed in an ideal engine?

Vedclass Test Series

Exam Paper Generator

Online Exam Module