The tire on a bicycle stored in a cool garage at 18 °C had a pressure of 80. psi. What is the pressure inside the tire after riding the bike at 43 °C?

Question

The tire on a bicycle stored in a cool garage at 18 °C had a pressure of 80. psi. What is the pressure inside the tire after riding the bike at 43 °C?
Analysis
Since this question deals with pressure and temperature, Gay–Lussac’s law is used to determine a final pressure because three quantities are known—the initial pressure and temperature ([latex]P_{1}[/latex] and [latex]T_{1}[/latex] ), and the final temperature ([latex]T_{2}[/latex] ).

Accepted Answer

[1] Identify the known quantities and the desired quantity.

[latex]P_{1}[/latex] = 80. psi
[latex]T_{1}[/latex] = 18 °C [latex]T_{2}[/latex]= 43 °C [latex]P_{2}[/latex] = ?
known quantities desired quantity

• Both temperatures must be converted to Kelvin temperatures.
• [latex]T_{1}[/latex]= °C + 273 = 18 °C + 273 = 291 K
• [latex]T_{2}[/latex]= °C + 273 = 43 °C + 273 = 316 K

[2] Write the equation and rearrange it to isolate the desired quantity, [latex]P_{2}[/latex], on one side.
• Use Gay–Lussac’s law. Since the initial pressure is reported in psi, the final pressure will be calculated in psi.

[3] Solve the problem.
• Substitute the three known quantities into the equation and solve for [latex]P_{2}[/latex].

• Since the temperature has increased, the pressure of the gas must increase as well.

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