Change in Vrms, given initial P and V, find energy added.

[MattRob]

Homework Statement

One mole of an ideal diatomic gas with $C_{v} = \frac{5R}{2}$ occupies a volume $Vi = 2.14 m^{3}$ at a pressure $P_{i}=1 atm$. The gas undergoes a process in which the pressure is proportional to the volume. At the end of the process, it is found that the rms speed of the gas molecules has doubled from its initial value. Determine the amount of energy transferred to the gas by heat.

Homework Equations

? (If I knew this, I wouldn't be here)

The Attempt at a Solution

With some searching, I found the equations $V_{rms} = \sqrt{\frac{3RT}{M}}$ and $Q = MC_{v}\Delta T$

Where $Q$ is a change in energy, $V_{rms}$ is the average rms velocity, $T$ is temperature, $M$ is Molar Mass, and $\Delta T$ is change in temperature.

With some substitution, we eventually found that we can get;
$Q = M^{2}V_{rms_{initial}}^{2} \frac{5}{2}$

Which... Doesn't help at all. So, yeah.

The question mentions that the pressure is proportional to the volume, but I'm still a bit confused about PV diagrams, and why everything doesn't stay on Isotherms, so I'm really not sure what it means when it says that pressure is proportional to volume. Does it mean $kP = V$ or $\frac{P}{V} = 1$, or what? So... Yeah.

 

[MattRob]

Problem solved. Got some unexpected help.