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.
[tex]PV=nRT[/tex]
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:
[tex](1.6atm)\times (18L)=(1mol)\times (0.0831451L.atm/mol.K)\times T[/tex]
[tex]T=346.4K[/tex]
The expression used for work done in reversible isothermal expansion will be,
[tex]w=nRT\ln (\frac{V_2}{V_1})[/tex]
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
[tex]V_1[/tex] = initial volume of gas = ?
[tex]V_2[/tex] = final volume of gas = 18 L
Now put all the given values in the above formula, we get:
[tex]3668J=1mole\times 8.31451J/mole.K\times 346.4K\times \ln (\frac{18L}{V_1})[/tex]
[tex]V_1=5.04L[/tex]
Therefore, the initial volume of gas will be 5.04 L.
