A quantity of gas with an initial volume of 1 cubic foot and a pressure of 500 psi expands to a volume of 2 cubic feet. Find the work done by the gas...Hint: Find K First...Please help!

Question

anonymous · Answer

Do you know the formula?

anonymous · Answer

Do you use something like: $$
PV = kT
$$

anonymous · Answer

I know its W= the integral from V1 to V0 of K/V dV

anonymous · Answer

Or that P=k/V

anonymous · Answer

Oh, so we can assume temperature does not change?

anonymous · Answer

I know the pressure varies inversely as volume.

anonymous · Answer

Okay so it really is just $$
P(V) = \frac{K}{V} \implies K = PV
$$And that means work is:
$$
W = \int_{V_1}^{V_2} P(V) dV = \int_{V_1}^{V_2} \frac{K}{V} dV = K\left[\ln(V)\bigg|_{V_1}^{V_2}\right] = K\ln\left(\frac{V_2}{V_1}\right) = P_1V_1\ln\left(\frac{V_2}{V_1}\right)
$$

anonymous · Answer

We could technically use any pair of $P$ and $V$ at any moment, but since we are given the initial pressure and volume, we'll use those.

anonymous · Answer

Okay so I will just replace P1 with 500 psi and V1 with 2ft^3?

anonymous · Answer

Yeah...

anonymous · Answer

Okay but that will give me some really crazy answer! Are you sure?

anonymous · Answer

Umm, you have to be careful about your units.

anonymous · Answer

Okay well what do you think the best units to use would be?