Question

One mole of ideal gas follows a law according to that it's pressure varies with volume as p= $\frac{a}{1+\frac{v}{b}}$where a and b are positive constant the temperature of the gas at volume v= a is

Answer 1

Step 1: Given

Pressure, P= $\frac{a}{1+\frac{v}{b}}$

Step 2: Formula used

$PV=nRT$

$P=\frac{nRT}{V}$

Step 3: Finding temperature

For one mole, n=1

$\therefore \frac{RT}{V}=\frac{a}{1+\frac{v}{b}}$

For v=a

$\frac{RT}{a}=\frac{a}{1+\frac{a}{b}}$

$T=\frac{a^2}{R(1+\frac{a}{b})}$

$T=\frac{a^{2}b}{R(a+b)}$

So, the temperature is $\frac{a^{2}b}{R(a+b)}$ .