Chapter 5, Problem 22P

Interpretation Introduction

Interpretation:

The new pressure should be determined if the gas is compressed to $\text{23}\text{.52 L}$ and the temperature is decreased to $\text{281 K}$

Concept Introduction:

The final temperature of the gas at the varying temperature and varying pressures can be calculated using combined gas law, which states the relationship between pressure, volume and temperature of the gas.

In combined gas law, the three laws of the gas are combined. Mathematically, it is given as.

$\frac{\text{PV}}{\text{T}}\text{=constant=k}$

We two different sets of temperature and pressure of the gas is considered, the above equation becomes as follows:

$\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}$

where ${\text{P}}_{\text{1}}$, ${\text{V}}_{\text{1}}$ and ${\text{T}}_{\text{1}}$ are initial pressure, volume and temperature of the gas, while ${\text{P}}_{\text{2}}$, ${\text{V}}_{\text{2}}$ and ${\text{T}}_{\text{2}}$ are final pressure, volume and temperature of the gas.