Question

A gas initially $20\text{kPa}$, $1.5\text{L}$ and $260\text{K}$ expands at constant temperature until the pressure drops to $12\text{kPa}$. The gas is then held at the constant pressure of $12\text{kPa}$ and heated until the temperature rises to $320\text{K}$. Calculate the final volume of the gas in litres.​

• A. 3.077

Answer 1

The correct option is A 3.077
Given:
At the constant temperature of $260\text{K}$, using Boyle's law:

${\text{P}}_1{\text{V}}_1={\text{P}}_2{\text{V}}_2$

${\text{V}}_2=\frac{{\text{P}}_1}{{\text{P}}_2}{\text{V}}_1$

$⟹\frac{20\times {10}^3}{12\times {10}^3}\times 1.5=\frac{30}{12}$

${\text{V}}_2=\frac{5}{2}=2.5\text{L}$

Now, at the constant pressure of $12\text{kPa}$, using Charles' law:

$\frac{{\text{V}}_1^{\ast }}{{\text{T}}_1}=\frac{{\text{V}}_2^{\ast }}{{\text{T}}_2}$

${\text{V}}_2^{\ast }=\frac{{\text{T}}_2}{{\text{T}}_1}{\text{V}}_1^{\ast }$

$⟹\frac{320}{260}\times 2.5=\frac{40}{13}$

${\text{V}}_2^{\ast }=3.07692\text{L}\approx 3.077\text{L}$

$\therefore$ The final volume of the gas is $3.077\text{L}$.