19. Neon gas of a given mass expands isothermally to
double volume. What should be the further fractional
decrease in pressure, so that the gas when
adiabatically compressed from that state, reaches the
original state?
(1) 1-2^-2/3
(2) 2^1/3
(3) 1 -3^1/3
(4) 3^2/3
Answers
Answer:
Option A is correct..... ❤
Explanation:
option A is correct answer
Answer: 1-2^{-\frac{2}{3}}1−2
−
3
2
Explanation:
Let initial Pressure and Volume be P₁ and V₁
After Isothermal expansion, the final pressure and volume be P₂ and V₂
For isothermal expansion, Temperature, T = constant.
⇒P₁V₁=P₂V₂
⇒P₁V₁=P₂(2V₁)
⇒P₂=P₁/2
After adiabatic compression, let the final pressure and volume be P₃ and V₃
P_2V_2^\gamma =P_3V_3^\gammaP
2
V
2
γ
=P
3
V
3
γ
where, the adiabatic index, \gamma = \frac{5}{3}γ=
3
5
for Neon
{P_3}{V_3}^\frac{5}{3}=P_1V_1^\frac{5}{3}P
3
V
3
3
5
=P
1
V
1
3
5
P_3(2V_1)^\frac{5}{3}=P_1V_1^\frac{5}{3}P
3
(2V
1
)
3
5
=P
1
V
1
3
5
P_3=2^{-\frac{5}{3}}P
3
=2
−
3
5
Fractional decrease in pressure so that gas is adiabatically compressed to same state is:
\frac{P_2-P_3}{P_2}=\frac{P_1/2-2^{-\frac{5}{3}}P_1}{P_1/2}=1-2^{-2/3}
P
2
P
2
−P
3
=
P
1
/2
P
1
/2−2
−
3
5
P
1
=1−2
−2/3
Hence, there should be 1-2^{-2/3}1−2
−2/3
decrease in pressure so that gas when adiabatically compressed from that state, reaches original state.