Chapter 8, Problem 8.94CQ

Interpretation Introduction

Interpretation:

“The temperature in degree Celsius in planet X” 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:

Volume of the balloon inside the space station, ${\text{V}}_{\text{1}}\text{= 850}\text{mL}$

Pressure inside the space station, ${\text{P}}_{\text{1}}\text{=755}\text{mmHg}$

Temperature inside the space station, ${\text{T}}_{\text{1}}{\text{= 24}}^{\text{0}}\text{C}$

Atmospheric pressure of planet X, ${\text{P}}_{\text{2}}\text{= 0}\text{.150}\text{atm}$

Volume of the balloon in planet X, ${\text{V}}_{\text{2}}\text{=3}\text{.22}\text{L}$