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The gases in a hair spray can are at a temperature of 27oC and a pressure of 30 lbs/in2. If the
gases in the can reach a pressure of 90 lbs/in2, the can will explode. To what temperature must
the gases be raised in order for the can to explode? Assume constant volume. Show your work.

Sagot :

  • P1=30lb/in^2
  • P2=90lb/in^2
  • T1=27°C
  • T2=?

Using Gay Lussac's Law

[tex]\boxed{\sf \dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{30}{27}=\dfrac{90}{T_1}[/tex]

[tex]\\ \sf\longmapsto T_1=\dfrac{90\times 27}{30}[/tex]

[tex]\\ \sf\longmapsto T_1=81°C[/tex]

Key Notes:-

Gay Lussac's Law:-

It states that at constant volume (V),The pressure(P) of fixed amount of gas caries directly with its absolute temperature(T).

[tex]\\ \sf\longmapsto P\propto T[/tex]

[tex]\\ \sf\longmapsto \dfrac{P}{T}=Constant[/tex]

[tex]\\ \sf\longmapsto \dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}[/tex]

[tex]\\ \sf\longmapsto P_1T_2=P_2T_1[/tex]

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