Question

An open vessel at $27°\mathrm{C}$ is heated until $3/5^{\mathrm{th}}$ of the air in it has been expelled. Assuming that the volume of the vessel remains constant, find the temperature to which the vessel has been heated?

Answer 1

Charles's law:

• When pressure is maintained constant, the volume of a fixed amount of dry gas is directly proportional to its absolute temperature, according to Charles' law.
• When two measurements are in direct proportion, every change in one of them has an immediate effect on the other.
• As the vessel is open, both volume and pressure are constant, hence the product of PV is constant.
• Mathematically, Charles’ law can be expressed as :
• $\frac{\mathrm{P}}{\mathrm{V}}=\mathrm{constant}$

Step 1: Analyzing given quantities

• Given $$\begin{gathered} {\mathrm{n}}_1=1 \\ {\mathrm{n}}_2=1-\frac{3}{5}=\frac{2}{5} \end{gathered}$$
• Here n is no. of moles

Step 2: simplifying the formula

• $$\begin{gathered} {\mathrm{n}}_1{\mathrm{RT}}_1={\mathrm{n}}_2{\mathrm{RT}}_2 \\ \mathrm{or}{\mathrm{n}}_2{\mathrm{n}}_1={\mathrm{T}}_1{\mathrm{T}}_2 \end{gathered}$$
• Inserting values into the equation.
• $$\begin{gathered} \frac{5}{2}=\frac{{\mathrm{T}}_2}{300} \\ \mathrm{or}{\mathrm{T}}_2=750\mathrm{K}\mathrm{or}477°\mathrm{C} \end{gathered}$$

So, the temperature to which the vessel has been heated to $750\mathrm{K}$