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 gasses 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)=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=300K`.
(c) If T is raised by 1K from 300K, find the `%` change in the speed of sound in the gaseous mixture.
(d) The mixtrue is compressed adiabatically to `1//5` of its initial volume V. Find the change in its adaibatic compressibility in terms of the given quantities.

Options

A. 1mole
B. 3 moles
C. 4 moles
D. 2 moles

Answer

D

Explanation

`C_(p)-C_(v)=R c_(V_(A))=R/(5/3-1)=3/2R`
`(C_(p))/(C_(v))=gamma . G_(P_(A))=5/2R`
`C_(v)=R/(gamma-1) C_(v_(B))=R/(7/5-1)=(5R)/2`
`C_(P)=(gamma-1) C_(v_(B))=R/(7/5-1)=(5R)/2`
`C_(P)=(gamma R)/(gamma-1)C_(p_(B))=(7R)/2`
`19/13=((1xxc_(p_(A))+n_(B)Cc_(p_(B)))/(1+n_(B)))/((1xxc_(v_(A))+n_(B)c_(v_(B)))/(1+n_(B)))`
`=L> n_(B)=2` moles