Chapter 11, Problem 52E

Interpretation Introduction

Interpretation: The temperature of the balloon at the mountaintop is to be calculated.

Concept Introduction: The combined gas law is a combination of Charles’s law and Boyle’s Law.

The Charles’s law states the relation between volume and temperature. According to Charles’s law, the volume is directly proportional to temperature.

The Boyle’s law states the relation between pressure and volume. According to Boyle’s Law, the pressure is inversely proportional to volume.

Therefore, the combined gas law combines both laws to give the equation is:

$\begin{array}{c}V\propto T\\ P\propto \frac{1}{V}\\ \frac{PV}{T}=\text{constant}\\ \frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}\end{array}$

For two different measurements, the combined gas law equation is:

Here, $V,T,P$ are volume, temperature, and pressure respectively. Also, $k$ is constant.