Question

A sample of nitrogen gas expands in volume from 1.3 to 5.7 L at constant temperature. Calculate the work done in joules if the gas expands (a) against a vacuum: J (b) against a constant pressure of 0.60 atm: × 10 J Enter your answer in scientific notation. (c) against a constant pressure of 4.7 atm: × 10 J Enter your answer in scientific notation.

Answer 1

Answer:

a) 0 J

b)  -2.67x10² J

c) -2.09x10³ J

Explanation:

For an isothermic expansion (with constant temperature) the work (W) is :

W = -pΔV, where p is the pressure and ΔV the volume variation. The minus signal is used because the compression is positive and ΔV is negative (Vf < Vi).

a) In vacuum, the relative pressure is 0 atm, so the work:

W = -0x(5.7 - 1.3)

W = 0 J

b) For a constant pressure of 0.60 atm

W = -0.6atmx(5.7 - 1.3)L = -2.64 L.atm

1 L.atm = 101.3 J

W = -2.64x101.3 = -2.67x10² J

c) For a pressure of 4.7 atm

W = -4.7atmx(5.7 - 1.3) L = - 20.68 atm.L

1 atm.L = 101.3 J

W = -20.68x101.3 = -2.09x10³ J