Consider a container with a frictionless piston that contains a given amount of

Question

Consider a container with a frictionless piston that contains a given amount of an ideal gas. Let's assume that initially the external pressure is 2.20 bar, which is the sum of a 1 bar atmospheric pressure and the pressure created by a very large number of very small pebbles that rest on top of the piston. The initial volume of gas is 0.500 L and the initial temperature is 25 degree C. Now, you will increase the volume of the gas by changing the external pressure slowly in a way that guarantees that the temperature of the system remains constant throughout the process. To do this, imagine you remove the pebbles one by one slowly to increase the volume by an infinitesimal amount. Every time you remove a weight you allow the system to equilibrate. Your cylinder is immersed in a water bath at 25 degree C, which keeps your gas at the same temperature throughout the whole process. Remember to use three significant figures for all numerical answers. The margin of error for each numerical answer is 1%. To avoid rounding errors use the unrounded intermediate values in your final calculations. What is the volume of the gas when you remove all pebbles? What is the final pressure of the gas?

Explanation / Answer

Equation of work done in an isothermal process is

W = nRT ln(V2/V1) which is equal to = nRT ln(P1/P2)

RHS = LHS , so,  ln(V2/V1) =  ln(P1/P2).

Or, exp(ln(P1/P2)) = V2/V1.

i.e P1/P2 = V2/V1.

1/2.20 = 0.500/V1.

V1 = 0.500×2.20 = 1.10.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.