Chapter U3.13, Problem 6E

Interpretation Introduction

Interpretation:

The pressure in the given nitrogen tank needs to be determined if after several hours the temperature rises to ${\text{55 }}^{\text{o}}\text{C}$ .

Concept introduction:

The law which states the relation between pressure, P and absolute temperature, T under constant volume, V is said to be Gay-Lussac's Law. According to this law, the pressure of an ideal gas has a direct relation with its absolute temperature:

$P\propto T$

Answer to Problem 6E

The pressure in the given nitrogen tank is $\text{164 atm}$ .

Explanation of Solution

Given:

Initial:

Temperature = ${\text{27 }}^{\text{o}}\text{C}$

Pressure = $150\text{ atm}$

The Gay-Lussac's Law can be expressed as for two different sets of condition for the same substance at constant volume as:

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Where 1 and 2 indicate conditions at set 1 and condition at set 2.

Converting the temperature values from degree Celsius to Kelvin as:

$T_1\text{ = 27 + 273}\text{.15 = 300}\text{.15 K}$

$T_1\text{ = 55 + 273}\text{.15 = 328}\text{.15 K}$

The value of $P_1\text{ = }150\text{ atm}$. Substituting these values as:

$\begin{array}{l}\frac{\text{150 atm}}{\text{300}\text{.15 K}}\text{ = }\frac{P_2}{328.15\text{ K}}\\ P_2\text{ = }\frac{\text{150 atm}\times 328.15\text{ K}}{\text{300}\text{.15 K}}\\ P_2\text{ = 163}\text{.99 atm }\simeq \text{ 164 atm}\end{array}$

Hence, the pressure in the given nitrogen tank is $\text{164 atm}$ .