Question

Be sure to answer all parts. A sample of nitrogen gas expands in volume from 1.8 to 4.7 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 0.96 atm: × 10 J Enter your answer in scientific notation. (c) against a constant pressure of 6.9 atm: × 10 J Enter your answer in scientific notation.

Answer 1

Given

Initial volume = 1.8 L(V1)

Final volume = 4.7 L (V2)

Work done in an isothermal expansion is

W=−pΔV

ΔV = change in volume = V2 - V1 = 4.7 L - 1.8 L = 2.9 L

(a)

Against a vacuum

As there is no pressure in a vacuum

P=0,

So no work is done.

w= - 0 atm * 2.9L = 0 L*atm = 0 J

Here we will be getting the answer in L atm but we need the answer in J

Hence

1L*atm = 101.3J

(b)

against a constant pressure of 0.96 atm

w= - 0.96 atm * 2.9L = -2.784 L*atm

w = -2.784 L*atm (101.3J/L*atm) = -282.02 J = -2.82 * 10² J

(C)

against a constant pressure of 6.9 atm

w= - 6.9 atm * 2.9L = -20.01 L*atm

w = -20.01 L*atm (101.3J/L*atm) = -2027.01 J = -2.03 * 10³ J