Question 464: Thermodynamics & KTG

Question

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

Accepted Answer

${T_1}{V^{\gamma  - 1}} = {T_2}{\left( {32V} ight)^{\gamma  - 1}}$
$ \Rightarrow {T_1} = {\left( {32} ight)^{\gamma  - 1}}.{T_2}$
For diatomic gas, $\gamma  = {7 \over 5}$
$	herefore$ $\gamma  - 1 = {2 \over 5}$
$	herefore$ ${T_1} = {\left( {32} ight)^{{2 \over 5}}}.{T_2} \Rightarrow {T_1} = 4{T_2}$
Now, efficiency $ = 1 - {{{T_2}} \over {{T_1}}}$
$ = 1 - {{{T_2}} \over {4{T_2}}}$
$ = 1 - {1 \over 4}$
$ = {3 \over 4}$
$ = 0.75.$

Answer

$0.5$

Answer

$0.75$

Answer

$0.99$

Answer

$0.25$

Thermodynamics & KTG

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

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