Question

One mole of helium is heated at $0^o$C and constant pressure. How much heat is required to increase its volume threefold?

• A. $3820cal$
• B. $382cal$
• C. $38.2cal$
• D. $3.28cal$

Answer 1

Answer: (A)

$3820cal$

As it is a constant pressure process, using Charles law we get $\frac{V}{T}=constant$. Thus for a threefold increase in volume we get threefold increase in temperature. Thus we get the final temperature as $3\left(273\right)=819K.$ Thus $\Delta T=819-273=546K$.
Now as helium is a diatomic molecule, its degree of freedom f is 5. Ths we get $C_p$ for it as $(1+\frac{f}{2})R=(1+\frac{5}{2})R=\frac{7}{2}R$.
Thus heat transferred will be given as $\Delta Q=n{C}_p\Delta T$
or
$\Delta Q=1(\frac{7}{2}\left)\right(1.987\left)\right(546)=3820cal$