A monoatomic gas (γ =5/3) at pressure P is suddenly compressed to (1/8) th of its volume adiabatically, the pressure of gas is :

Question

A monoatomic gas (&gamma; =5/3) at pressure P is suddenly compressed to (1/8) th of its volume adiabatically, the pressure of gas is : (A)  (43/3)P  (B)  8P  (C)  32 P  (D)  (24/5)P

Tardigrade Admin · Accepted Answer

The condition that must be obeyed by an ideal gas in an adiabatic process is given by

P V^{γ} =

constant
or

P_{1} V_{1}^{γ} = p_{2} V_{2} γ

or

P_{2} = P_{1} (\frac{V _{1}}{V _{2}})^{γ}

Here,

P_{1} = P, \frac{V _{2}}{V _{1}} = \frac{1}{8}, γ = \frac{5}{3}

∴ P_{2} = P (8)^{5/3}

or

P_{2} = P (2^{3})^{5/3} = 32 P

Note: The equation

P V^{γ} =

constant can be written in terms of other pair of thermodynamic variables by combining it with the ideal gas law

(P V = n RT)

. In doing so, we will find that,

T V^{γ - 1} =

constant and

T^{γ} P^{1 - γ} =

constant.

Q. A monoatomic gas $(γ = 5/3)$ at pressure P is suddenly compressed to $\frac{1}{8}$ th of its volume adiabatically, the pressure of gas is :

$\frac{43}{3} P$

$8 P$

$32 P$

$\frac{24}{5} P$

Q. A monoatomic gas (γ=5/3) at pressure P is suddenly compressed to 81​ th of its volume adiabatically, the pressure of gas is :

343​P

8P

32P

524​P

Q. A monoatomic gas $(γ = 5/3)$ at pressure P is suddenly compressed to $\frac{1}{8}$ th of its volume adiabatically, the pressure of gas is :

$\frac{43}{3} P$

$8 P$

$32 P$

$\frac{24}{5} P$