Question

One mole of an ideal gas does 3668 J of work on the surroundings as it expands isothermally to a final pressure of 1.6 atm and volume of 18 L. Find the initial volume. The universal gas constant is 8.31451 J/K · mol. Answer in units of L.

Answer 1

Answer : The initial volume of gas will be 5.04 L.

Explanation :

First we have to calculate the temperature of gas by using ideal gas equation.

`PV=nRT`

where,

P = pressure of gas = 1.6 atm

V = volume of gas = 18 L

n = number of moles of gas = 1 mol

R = gas constant = 8.31451 J/K.mol = 0.0831451 L.atm/mol.K

Now put all the given values in the above formula, we get:

`(1.6atm)* (18L)=(1mol)* (0.0831451L.atm/mol.K)* T`

`T=346.4K`

The expression used for work done in reversible isothermal expansion will be,

`w=nRT\ln ((V_2)/(V_1))`

where,

w = work done = 3668 J

n = number of moles of gas = 1 mole

R = gas constant = 8.31451 J/mole.K

T = temperature of gas = 346.4 K

`V_1` = initial volume of gas = ?

`V_2` = final volume of gas = 18 L

Now put all the given values in the above formula, we get:

`3668J=1mole* 8.31451J/mole.K* 346.4K* \ln ((18L)/(V_1))`

`V_1=5.04L`

Therefore, the initial volume of gas will be 5.04 L.