Question

A bicycle tire is filled with air to a pressure of 100. psi at a temperature of 19C. Riding the bike on asphalt on a hot day increases the temperature of the tire to 58?C. The volume of the tire increases by 4.0%. What is the new pressure in the bicycle tire?

Answer 1

Answer:

108.9897 psi

Explanation:

Using Ideal gas equation for same mole of gas as

$\frac {{P_1}\times {V_1}}{T_1}=\frac {{P_2}\times {V_2}}{T_2}$

Given ,  

Let V₁ = x units

The new volume increases by 4 % which means

V₂ = x + 0.04x = 1.04 x

P₁ = 100 psi

P₂ = ?

T₁ = 19 ºC

T₂ = 58 ºC

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15  

So,  

T₁ = (19 + 273.15) K = 292.15 K  

T₂ = (58 + 273.15) K = 331.15 K  

Using above equation as:

$\frac {{P_1}\times {V_1}}{T_1}=\frac {{P_2}\times {V_2}}{T_2}$

$\frac {{100}\times {x}}{292.15}=\frac {{P_2}\times {1.04x}}{331.15}$

Solving for P₂ , we get:

P₂ = 108.9897 psi