Given:
The initial volume of the gas, V₁=3200 ml=3.2×10⁻³ m³
The initial pressure of the gas, P₁=122 kPa
The initial temperature of the gas, T₁=27 °C=300 K
The final temperature, T₂=65 °C=338 K
The final pressure, P₂=112 kPa
To find:
The final volume of xenon gas.
Explanation:
From the combined gas law,
![\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}](https://tex.z-dn.net/?f=%5Cfrac%7BP_1V_1%7D%7BT_1%7D%3D%5Cfrac%7BP_2V_2%7D%7BT_2%7D)
Where V₂ is the volume after it is heated.
On rearranging the above equation,
![V_2=\frac{T_2P_1V_1}{T_1P_2}](https://tex.z-dn.net/?f=V_2%3D%5Cfrac%7BT_2P_1V_1%7D%7BT_1P_2%7D)
On substituting the known values,
![\begin{gathered} V_2=\frac{338\times112\times10^3\times3.2\times10^{-3}}{300\times112\times10^3} \\ =3.61\text{ m}^3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20V_2%3D%5Cfrac%7B338%5Ctimes112%5Ctimes10%5E3%5Ctimes3.2%5Ctimes10%5E%7B-3%7D%7D%7B300%5Ctimes112%5Ctimes10%5E3%7D%20%5C%5C%20%3D3.61%5Ctext%7B%20m%7D%5E3%20%5Cend%7Bgathered%7D)
Final answer:
The volume of the balloon when it is heated is 3.61 m³