A gaseous mixture enclosed in a vessel of volume consists of one mole of a gas with…

PHYSICS · Multi-part · CBSE · Physics · Kinetic Theory · Kinetic Theory

Problem

A gaseous mixture enclosed in a vessel of volume

V

consists of one mole of a gas

A

with

\gamma (=C_p/C_v) = 5/3

and another gas

B

with

\gamma = 7/5

at a certain temperature

T

. The relative molar masses of the gases

A

and

B

are 4 and 32, respectively. The gases

A

and

B

do not react with each other and are assumed to be ideal. The gaseous mixture follows the equation

PV^{19/13} = \text{constant}

in adiabatic processes. (a) Find the number of moles of the gas

B

in the gaseous mixture. (b) Compute the speed of sound in the gaseous mixture at

T = 300 \text{ K}

. (c) If

T

is raised by

1 \text{ K}

from

300 \text{ K}

, find the % change in the speed of sound in the gaseous mixture. (d) The mixture is compressed adiabatically to

1/5

of its initial volume

V

. Find the change in its adiabatic compressibility in terms of the given quantities.