We have some gas in a container at high pressure. The volume of thecontainer is

ID: 1757865 • Letter: W

Question

500 cm3 . The pressure of the gas is 2.52 × 10 raised tothe 5th Pa. We allow the gas to expand

at constant temperature until its pressure is equal to theatmospheric pressure, which at

the time is 0.857 × 10 raised to the 5th Pa. (a)Find the work (J) done on the gas. (b) Find the change of

internal energy (J) of the gas. (c) Find the amount of heat (J) weadded to the gas to

keep it at constant temperature. Be sure to include the correctsigns on the answers.

We have some gas in a container at high pressure. The volume of thecontainer is 500 cm3 . The pressure of the gas is2.52 × 10

raised to the 5th Pa. We allow the gas to expand at constanttemperature until its pressure is equal to the atmosphericpressure, which at

the time is 0.857 × 10 raised to the5th Pa.

(a) Find the work (J) done on the gas.

answer:

since the T is constant, PV = constant = (=nRT)

initial P = P1 = 2.52 x 10^5

initial volume = V1 = 500 cm^3 = .0005 m^3

final P = P2 = .857 x 10^5

so final volume V2 is given by

( .857 x 10^5) V2 = (2.52 x 10^5)(.0005 m^3)

V2 = .00147 m^3

= P1V1 = 126

work done by gas = (int)[PdV] = (int)[(/V) dV] = ln(V2/V1)

= 126 ln (.00147/.0005) = 135.88 J

work done on gas = - 135.88 J

(b) Find the change of internal energy (J) of the gas.

the internal energy is only a function of T. since T does notchange,

change in internal energy = 0 J

from conservation of energy, the amount of heat needed is

Q = W = 135.88 J

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