Question

10 moles of oxygen $(O_2$) gas is being expanded in a container, maintained at a constant pressure, by supplying 500J of heat. What is the rise in the gas' temperature? Assume the atoms do not oscillate along the bond axis, and the gas is pretty much ideal

• A. 1.72 K
• B. 24.7 K
• C. 2.35 K
• D. 8.64 K

Answer 1

Answer: (A)

1.72 K

The oxygen molecules can undergo translational motion in three unique dissections (along x, y and z axes), and rotate about two different axes (as encountered in the previous problem). It, therefore, has five degrees of freedom in total.

Since, according to the equipartition theorem,

$C_V=\left[\frac{numberofdegreesoffreedom}{2}\right]\times R$,

and we already know,

$C_P-C_V=R$,

We can write $C_P$ as -

$C_P=C_V+R$

= $\frac{5}{2}R+R$

= $\frac{7}{2}R$.

$\therefore Q=n{C}_P\Delta T$

$\Rightarrow \Delta T=\frac{Q}{n{C}_P}$

$\Rightarrow \Delta T=\left[\frac{500}{10\times \frac{7}{2}\times 8.314}\right]K$

$\Rightarrow \Delta T=1.72K$.