Question

Three moles of an ideal gas expanded spontaneously into vacuum. The work done will be:
a.) Infinite
b.) 3 Joules
c.) 9 Joules
d.) zero

Answer 1

Hint:. The work done is the product of pressure and the change in volume. The ideal gases expand spontaneously into vacuum if the external pressure will be zero.

Complete step by step answer:
The work done during the free expansion of an ideal gas is always zero when the process is irreversible. Given in the question that an ideal gas expands spontaneously into vacuum.
Work done is the product of pressure and the change in volume, the expression for work done will be:
Work done = $-P\Delta V$
Where, P = external pressure
And $\Delta V$= the change in volume
Now, the ideal gas expands spontaneously in vacuum hence the external pressure will be zero
Work done = $-(0)X\Delta V$= 0
Hence the work done = 0
So, the correct answer is “Option D”.

Work done is calculated differently for different process for example for a reversible isothermal process work done is expressed as
\[W=-nRT\ln \dfrac{{{V}_{2}}}{{{V}_{1}}}\]
Where, n = number of moles of the gases
R = universal gas constant
${{V}_{1}}\text{ and }{{\text{V}}_{2}}$ = initial and final Volume respectively
In case of the irreversible adiabatic free expansion the change in enthalpy will depend on the sum of the internal energy change and the temperature will also be zero.

Note: It is important to remember that the free expansion of a gas takes place only when the gas is subjected to expand against zero pressure. So if it is mentioned that the ideal gas expands in vacuum, it indicates that the work done or the expansion takes place against zero pressure.