Week 3,4 HW #14

[MaiVyDang2I]

A sample of an ideal gas in a cylinder of volume 3.73 L at 298 K and 2.89 atm expands to 8.82 L by two different pathways. Path A is an isothermal, reversible expansion. Path B has two steps. In the first step, the gas is cooled at constant volume to 1.42 atm . In the second step, the gas is heated and allowed to expand against a constant external pressure of 1.42 atm until the final volume is 8.82 L .

Calculate the work for path A and B.

Can somebody walk me through which values to plug in for the equation of path A and B?

[Ryan Khiev 1L]

Hi! For this problem, you need to utilize two equations: w = -(Pressure from external source)(Change in V) for irreversible expansion, and w = -nRT*ln(V2/V1) for reversible expansion, where R is equal to 8.314 J/K*mol.

A sample of an ideal gas in a cylinder of volume 3.73 L at 298 K and 2.89 atm expands to 8.82 L by two different pathways. Path A is an isothermal, reversible expansion. Path B has two steps. In the first step, the gas is cooled at constant volume to 1.42 atm . In the second step, the gas is heated and allowed to expand against a constant external pressure of 1.42 atm until the final volume is 8.82 L .

First, let's set up for Path A. Since we don't know the moles of gas to plug into w = -nRT*ln(V2/V1), we need to solve for it using the ideal gas equation, PV = nRT. (2.89atm)(3.73L) = n(8.206*10^-2)(298K). Then after solving for n, you would plug it into the above equation to solve for w.

Now, let's set up for Path B. Since we the gas is expanding against an external pressure of 1.42 atm, and the final and initial volumes are 8.82 L and 3.73 L, respectively, set up the equation as follows: w = -(1.42atm)(8.82L - 3.73L). This will give you the answer in atm*L, but since your answer should be in joules, use the conversion 101325J = 1atm*L to solve for the work done by the system.

Hope this helps!