Chapter 2, problem 3, parts c-e. Calculate the work (in J) done on the system fo

Question

Chapter 2, problem 3, parts c-e. Calculate the work (in J) done on the system for each of the following examples (the system is given in italics). Specify the sign of the work. The volume of an ideal gas changes from 1.00 L to 3.00 L at an initial temperature of 25 degree C and a constant pressure of 1 bar. The volume of an ideal gas changes from 1.00 L to 3.00 L at an initial temperature of 25 degree C and a constant pressure of 0.1 Pa. The volume of an ideal gas changes from 1.00 L to 3.00 L at a constant temperature of 25 degree C, and the expansion is done reversibly from an initial pressure of 1 bar.

Explanation / Answer

Answer – C) We are given, V1 = 1.0 L , V2 = 3.00 L , P = 1 bar = 0.987 atm

We know the formula

Work = -P*t

          = -0.987 atm *( 3.00-1.0 L )

          = -1.974 atm.L

We know , 1 J = 101.3 / atm.L

= -1.74 atm. L *101.3 J/L.atm

= -199.97 J

d) We are given, V1 = 1.0 L , V2 = 3.00 L , P = 0.1 Pa = 9.87*10-7 atm

We know the formula

Work = -P*t

          = -9.87*10-7 atm *( 3.00-1.0 L )

          = -1.974*10-7 atm.L

We know , 1 J = 101.3 / atm.L

= -1.974*10-7 atm.L *101.3 J/L.atm

= - 2.00*10-4 J

e) We know work done in the isothermal reversible expansion of the gas is

W = -nRT * ln V2/V1

    = -1 moles *8.314 J/mol.K *298 K*298 K* ln 3.0 L / 1.0 L

    = - 2722 J

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