Chapter 11, Problem 11.89AQAP

Interpretation Introduction

Interpretation:

The volume of balloon “if the amount of hydrogen remains the same” should be calculated.

Concept introduction:

Here, we are using the concept of different gaseous law which are combined to form a combined gaseous law.

► Boyle’s Law: It states that at constant temperature, the pressure of the gas has inverse relation with volume

$P\alpha \frac{1}{V}$

► Charles’ Law: It states that at constant pressure, the volume is directly proportional to the temperature

$V\alpha T$

► Gay-Lussac’s law: It states that at constant volume, the pressure of the gas has direct relation with temperature

$P\alpha T$

► Now by combining the three law we get a relationship between pressure, volume and temperature which is known as combined gas equation

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Given:

Initial volume of the balloon, $V_1=31000L$

Pressure, $P_1=755\text{mmHg}$

Temperature of the gas, $T_1={22}^{0}C$

At $1000\text{m}$ altitude

Pressure of the gas, $P_2=658\text{mmHg}$

Temperature of the gas, $T_2=-8^{0}C$