Chapter 15, Problem 9P

To determine

To find : The change in temperature.

Answer to Problem 9P

  $400.96$ kelvin

Explanation of Solution

Given:

Work $=7500$ J

  $n=3/2$ mole

  $f=3$ for monoatomic gas.

Formula Used :

For adiabatic process $\Delta U=W$

Calculation :

Substituting the values,

  $\frac{nf\Delta TR}{2}=W$

  $\frac{nf\Delta TR}{2}=7500$

  $\Rightarrow 3\times \frac{3}{2}\times R\times \frac{\Delta T}{2}=7500$

  $\Rightarrow 9R\Delta T=7500\times 4$

  $\Rightarrow \Delta T=\frac{7500\times 4}{9R}$

  $\Rightarrow \Delta T=\frac{30000}{9\times 8.214}=400.96$

  $\Rightarrow \Delta T=400.96$ kelvin