Question

A diatomic gas $(\gamma =1.4)$ of mass $m$ at a pressure of $2$ atmospheres is compressed adiabatically so that its temperature rises from ${27}^{\circ }\text{C}$ to ${927}^{\circ }\text{C}.$ The pressure of the gas in final state is

• A. $256\text{atm}$
• B. $8\text{atm}$
• C. $28\text{atm}$
• D. $68.7\text{atm}$

Answer 1

The correct option is A $256\text{atm}$

For a gas undergoing adiabatic process, equation of state interms of $P$ and $T$ is given by
$P^{1-\gamma }.T^{\gamma }=$ constant
$\Rightarrow P{T}^{\left(\frac{\gamma }{1-\gamma }\right)}=$ constant
Relation between initial and final states can be written as
$\frac{P_2}{P_1}={\left(\frac{T_2}{T_1}\right)}^{\frac{\gamma }{\gamma -1}}$
From the data given in the question,
$\frac{P_2}{2}={\left(\frac{1200}{300}\right)}^{\frac{1.4}{1.4-1}}$
$\Rightarrow P_2=2\times {\left(4\right)}^{\frac{7}{2}}$
$\Rightarrow P_2=2^8=256\text{atm}$
Hence, option (a) is the correct answer.