A container of 3.1 mol of gas expands from 1.5 L to 2.5 L (1 L = 0.001 m 3 ) whi

Question

A container of 3.1 mol of gas expands from 1.5 L to 2.5 L (1 L = 0.001 m3) while the pressure is kept constant. The gas is initially at a temperature of 290 K.

a) What is the pressure of the gas?
b)What is the final temperature of the gas?

c)What is the magnitude of the change in internal energy of the gas, and is the internal energy increasing or decreasing? (Note that there is no change in chemical energy because there is no reaction that occurs.)

d) What is the magnitude of the energy transferred as work, and is it transferred into or out of the gas?
e)What is the magnitude of the energy transferred as heat, and is it transferred into or out of the gas?

Explanation / Answer

Solution-Using the formula

PV = n R T

(P) (1.5 x 10^-3 m^3) = (3 mol) (8.314) (290)

P = 4.82 x 10^6 Pa  




V / T = constant

1.5 / 290 = 2.5 / Tf

Tf = 483.33K


deltaU = n Cv deltaT

= 3.1 x (3.1 x 8.314 /2) (483.33 - 285)

= 7923.04 J

increase


W = P deltaV = (4.82 x 10^6)(1 x 10^-3)

= 4820 J

out of gas


Q = n Cp deltaT

= 3 x(5 x8.314 / 2) (483.33 - 290)

= 12055.09 J

into the gas

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