Question

Calculate the maximum work done when pressure on $10g$ of hydrogen is reduced from $20atm$ to $1atm$ at a constant temperature of $273K$. The gas behaves ideally. Will there be any change in internal energy? Also calculate $q$.

Answer 1

moles of $H_2=\frac{10}{2}=5mol$

$p_1=20atm=p_2=1atm$

$\therefore$ work done in expansion = $RTln{p}_1/p_2$

$=\mathrm{8.3.4}\times 273ln\frac{20}{1}$

$=6799.47J/mol$

$\therefore$ for 5 mol of $H_2$ work done $=5\times 6799.47J$

$=33997.39J$

$=33.99739KJ$

$\therefore$ at constant temperature the inter energy change

is zero $△u=0,u=constant$

at isothermal process $△Q=△U+w$

$\Rightarrow △Q=w$

$=33.99739KJ$

$Q=-33.99739KJ$ (Ans)