A diatomic ideal gas is used in a Carnot engi | vedclass

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

Question

(C) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by $TV^{\gamma-1} = 	ext{constant}$.Thus,$T_H V_1^{\gam

Vedclass · Accepted Answer

$0.75$

Vedclass · Answer

(C) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by $TV^{\gamma-1} = 	ext{constant}$.Thus,$T_H V_1^{\gamma-1} = T_C V_2^{\gamma-1}$,where $T_H$ is the source temperature and $T_C$ is the sink temperature.Given that the gas is diatomic,the adiabatic index $\gamma = 1.4$.The volume changes from $V_1 = V$ to $V_2 = 32V$.Substituting these values:$\frac{T_C}{T_H} = \left(\frac{V_1}{V_2}ight)^{\gamma-1} = \left(\frac{V}{32V}ight)^{1.4-1} = \left(\frac{1}{32}ight)^{0.4}$.Since $32 = 2^5$,we have $\left(\frac{1}{2^5}ight)^{0.4} = \left(\frac{1}{2^5}ight)^{2/5} = \left(\frac{1}{2}ight)^2 = \frac{1}{4} = 0.25$.The efficiency of the Carnot engine is $\eta = 1 - \frac{T_C}{T_H}$.$\eta = 1 - 0.25 = 0.75$.

$A$ diatomic ideal gas is used in a Carnot engine as a working substance. If during the adiabatic expansion part of the cycle,the volume of the gas increases from $V$ to $32V$,the efficiency of the engine is:

Similar Questions

The temperature of food material in a refrigerator is $4^{\circ} C$ and the temperature of the environment is $15^{\circ} C$. If a Carnot cycle is used in its working gas,find its Carnot efficiency.

$A$ 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 $K$)

The efficiency of a Carnot heat engine is $25 \%$ and the temperature of its source is $127^{\circ} C$. Without changing the temperature of the source,if the absolute temperature of the sink is decreased by $10 \%$,the new efficiency of the engine is: (in $\%$)

In a heat engine,the temperature of the source and sink are $500\, K$ and $375\, K$. If the engine consumes $25\times10^5\, J$ per cycle,the work done per cycle is

The efficiency of a reversible engine is . . . . . . the efficiency of an irreversible engine.

Vedclass Test Series

Exam Paper Generator

Online Exam Module