During an adiabatic process, the cube of the pressure is found to be inversely proportional to the fourth power of the volume. Then, the ratio of specific heats is :

Question

During an adiabatic process, the cube of the pressure is found to be inversely proportional to the fourth power of the volume. Then, the ratio of specific heats is : (A) 1 (B) 1.33 (C) 1.67 (D) 1.4

Tardigrade Admin · Accepted Answer

P3 propto (1/ V4)⇒ P3V4= constant ⇒ PV4 / 3= constant Comparing with PV' ⇒ &gamma; =(4/3)=1.33

Q. During an adiabatic process, the cube of the pressure is found to be inversely proportional to the fourth power of the volume. Then, the ratio of specific heats is :

$1$

$1.33$

$1.67$

$1.4$

$P^{3} \propto \frac{1}{V ^{4}} \Rightarrow P^{3} V^{4} =$ constant
$\Rightarrow P V^{4/3} =$ constant
Comparing with $P V^{'}$
$\Rightarrow γ = \frac{4}{3} = 1.33$

Q. During an adiabatic process, the cube of the pressure is found to be inversely proportional to the fourth power of the volume. Then, the ratio of specific heats is :

1

1.33

1.67

1.4

P3∝V41​⇒P3V4= constant ⇒PV4/3= constant Comparing with PV′ ⇒γ=34​=1.33

$1$

$1.33$

$1.67$

$1.4$

$P^{3} \propto \frac{1}{V ^{4}} \Rightarrow P^{3} V^{4} =$ constant
$\Rightarrow P V^{4/3} =$ constant
Comparing with $P V^{'}$
$\Rightarrow γ = \frac{4}{3} = 1.33$