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Chapter 5: Problem 62

A bicycle tire is filled with air to a pressure of 75 psi at a temperature of \(19^{\circ} \mathrm{C}\) . Riding the bike on asphalt on a hot day increases the temperature of the tire to \(58^{\circ} \mathrm{C}\) . The volume of the tire increases by 4.0\(\%\) . What is the new pressure in the bicycle tire?

Short Answer

Expert verified
The new pressure in the bicycle tire is approximately \(79.64 \,\mathrm{psi}\).

Step by step solution

01

Convert Given Temperatures to Kelvin Scale

The Combined Gas Law uses the Kelvin temperature scale. So, we need to convert the given temperatures from Celsius to Kelvin: \(T_1 = 19^{\circ}\mathrm{C} + 273.15 = 292.15 \mathrm{K}\) \(T_2 = 58^{\circ}\mathrm{C} + 273.15 = 331.15 \mathrm{K}\)
02

Calculate the Volume Increase

The volume of the tire increases by 4%, so we need to find the relationship between initial and final volumes: \(V_2 = V_1 + 0.04V_1 = 1.04V_1\)
03

Apply the Combined Gas Law

While applying the Combined Gas Law, the terms related to volume and initial pressure will cancel out to get the final pressure. Substitute the known values and solve for \(P_2\): \(\frac{P_1V_1}{T_1}=\frac{P_2(1.04V_1)}{T_2}\) \(\frac{75(1)}{292.15}=\frac{P_2(1.04)}{331.15}\)
04

Solve for the Final Pressure

Next, we will isolate the final pressure, \(P_2\), by solving the equation: \(\frac{75(1)(331.15)}{292.15(1.04)} = P_2\) \(P_2 \approx 79.64 \,\mathrm{psi}\) Thus, the new pressure in the bicycle tire is approximately 79.64 psi.

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Most popular questions from this chapter

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