Question

Gas in a cylinder is maintained at $10$ atom pressure and $300$ K temperature. The cylinder will explode if pressure of gas exceeds $15$ atm. What is the maximum temperature at which gas can be heated?

Answer 1

Hint: Gay Lussac’s law states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas, when the volume is kept constant
$\dfrac{P}{T} = K$ or $P \propto T$
The pressure of an enclosed gas is directly proportional to its temperature at constant volume.
This law holds true because temperature is a measure of the average kinetic energy of a substance as the kinetic energy of a gas increases its particles collide with the container walls more rapidly there by exerting increased pressure
For comparing the same substance under two different sets of conditions, the law can be written as,
$\dfrac{{{P_1}}}{{{T_1}}} = \dfrac{{{P_2}}}{{{T_2}}}$or ${P_1}{T_2} = {P_2}T$

Complete step by step answer:
A cylinder containing an ideal gas maintained
Atmospheric pressure$\left( {{P_{\kern 1pt} }} \right) = 10$am and temperature $\left( {{T_1}} \right) = 300K$
The cylinder will get explode if pressure of gas belong
Atmospheric pressure $\left( {{P_2}} \right) = 15$atm.
According to Gay Lussac’s law comparing the gas particle under two different sets of condition
$
  \dfrac{{{P_1}}}{{{T_1}}} = \dfrac{{{P_2}}}{{{T_2}}} \\
  \therefore {T_2} = \dfrac{{{T_1}{P_2}}}{{{P_1}}} \\
  \therefore {T_2} = \dfrac{{30K \times 15m}}{{10atm}} \\
  \therefore {T_2} = 30 \times 15K \\
  \therefore {T_2} = 450K \\
 $

Note:
Gay Lussac name is now generally associated within chemistry with the law of combining volume. Gas – Lussac primarily investigated the relationship between volume and temperature but his work did cover some comparison between pressure and temperature. Gay Lussac was able to experiment with multiple types of common gases such as oxygen, nitrogen and hydrogen Gay Lussac’s law Charle’s law and Boyle’s law forms the combined gas law. These three gas laws in combination with Avogadro’s law can be generalized by the ideal gas law.