Question

An ideal gas, initially at a pressure of 11.2 atm and a temperature of 299 K, is allowed to expand adiabatically until its volume doubles.
Required:
What is the gas’s final pressure, in atmospheres, if the gas is diatomic?

Answer 1

Answer:

The pressure is  $P_2 = 4.25 \ a.t.m$

Explanation:

From the question we are told that

   The initial pressure is $P_1 = 11.2\ a.t.m$

   The  temperature is  $T_1 = 299 \ K$

   

Let the first volume be  $V_1$ Then the final volume will be  $2 V_1$

 Generally for a diatomic  gas

           $P_1 V_1 ^r = P_2 V_2 ^r$

Here r is the radius of the molecules which is  mathematically represented as

    $r = \frac{C_p}{C_v}$

Where $C_p \ and\ C_v$ are the molar specific heat of a gas at constant pressure and  the molar specific heat of a gas at constant volume with values

     $C_p=7 \ and\ C_v=5$

=>   $r = \frac{7}{5}$

=>  $11.2*( V_1 ^{\frac{7}{5} } ) = P_2 * (2 V_1 ^{\frac{7}{5} } )$

=>   $P_2 = [\frac{1}{2} ]^{\frac{7}{5} } * 11.2$

=>  $P_2 = 4.25 \ a.t.m$