Question

A tank with a movable piston having initial volume of $0.2{\text{m}}^3$ contains $He$ gas at a temperature of $300\text{K}$ and pressure ${10}^5{\text{N/m}}^2$. Find the amount of heat required to raise the temperature of gas to $400\text{K}$ at constant pressure. The molar heat capacity of $He$ at constant pressure is $5{\text{cal K}}^{-1}{\text{mol}}^{-1}$.

• A. $2400\text{cal}$
• B. $3800\text{cal}$
• C. $4000\text{cal}$
• D. $5000\text{cal}$

Answer 1

The correct option is C $4000\text{cal}$

Initial volume $\left(V\right)=0.2{\text{m}}^3$
$\Rightarrow$ The number of moles of gas in the tank will remain constant( tank is closed by piston),
$n=\frac{PV}{RT}$
$\therefore n=\frac{{10}^5\times 0.2}{8.31\times 300}=8\text{mol}$
The amount of heat required to raise the temperature of gas in tank at constant pressure is
$\Delta Q=n{C}_p\Delta T$
$Q=8\times 5{\text{cal mol}}^{-1}{\text{K}}^{-1}\times 100\text{K}$
$\therefore Q=4000\text{cal}$