Question 522: 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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