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.

Explanation

Let's solve the problem step by step.

### Given Data:
- Gas A:
- Number of moles, \( N_A = 1 \)
- \( \gamma_A = \frac{C_p}{C_v} = \frac{5}{3} \)
- Molar mass, \( M_A = 4 \, \text{g/mol} \)

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