Shows the initial state of an apparatus consisting of an ideal gas in a bulb, a

Question

Shows the initial state of an apparatus consisting of an ideal gas in a bulb, a stopcock, a porous plug, and a cylinder containing a frictionless piston. The walls arc diathermal. and the surroundings arc at a constant temperature of 300.0 K and a constant pressure of 1.00 bar. When the stopcock is opened, the gas diffuses slowly through the porous plug, and the piston moves slowly to the right. The process ends when the pressures arc equalized and the piston stops moving. The system is the gas. Assume that during the process the temperature throughout the system differs only infinitesimally from 300.0 K and the pressure on both sides of the piston differs only infinitesimally from 1.00 bar. Which of these terms correctly describes the process: isothermal, isobaric. isochoric. reversible, irreversible? Calculate q and w.

Explanation / Answer

(a) isothermal and revesible

(b) No. of moles of ideal gas, n = pV/ RT = 3 bar x 0.5 x 1000 L/ 8.314 x 10-2 L-bar-K-1 mol-1 x 300 K = 60.14 moles

As work done in reversible isothermal expansion is given by:

w= -nRT ln (P1/ P2) = 60.14 mol x (8.314 J K-1 mol-1) (300 K) ln (3 bar/ 1 bar) = - 164793.15 J

Since the process is Isothermal, therefore, U=0

From first law, U= q + w
Since U=0, q = – w = - (- 164793.15 J) = 164793.15 J

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