Question

For the isothermal expansion of an ideal gas into vaccum, the values of $\Delta U=x,q=y,w=z$. Find the value of $x\times y\times z$.

Answer 1

For an isothermal process, $\Delta T=0$
For an ideal gas, the internal energy $U$ depends only on the temperature and not on the pressure nor volume.
So, $\Delta U=0$
Based on the mathematical form of the first law,
$\Delta U=q+w\Rightarrow q=-w=-p\Delta V$
For the isothermal free expansion of an ideal gas into vacuum,
$p=0\therefore q=-w=0$
So, the correct value is $\Delta U=0,q=0,w=0$
Hence, $x\times y\times z=0\times 0\times 0=0$