Question

A vessel of volume $0.2m^3$ contains hydrogen gas at temperature $300K$ and pressure $1bar$. Find the heat required to raise the temperature to $400K$. The molar heat capacity of hydrogen at constant volume is $5cal/molK$.

• A. ${\left(\Delta Q\right)}_v=2.1kcal$
• B. ${\left(\Delta Q\right)}_v=4.2kcal$
• C. ${\left(\Delta Q\right)}_v=2kcal$
• D. ${\left(\Delta Q\right)}_v=4kcal$

Answer 1

The correct option is D ${\left(\Delta Q\right)}_v=4kcal$

As here volume of gas remains constant, we get
${\left(\Delta Q\right)}_v=\mu C_v\Delta T$
Here, $C_v=5cal/molK$
And $\Delta T=(400-300)=100K$
And so for ideal gas $PV=\mu RT$
$\mu =\frac{(10{)}^5\times (0.2)}{8.31\times 300}=8mol$
${\left(\Delta Q\right)}_v=8\times 5\times 100=4kcal$