What is the gauge pressure of a tire when its temperature increases from 20°C to 45°C and its volume increases by 5%?

To determine the gauge pressure of the tire after the temperature increases from 20°C to 45°C and its volume increases by 5%, we can apply the ideal gas law, which relates pressure, volume, and temperature. The law can be expressed as ( PV = nRT ), where ( P ) is pressure, ( V ) is volume, ( n ) is the number of moles of gas, ( R ) is the ideal gas constant, and ( T ) is the temperature in Kelvin.

First, convert the temperatures from Celsius to Kelvin:

• Initial temperature: ( 20°C = 293.15 K )

• Final temperature: ( 45°C = 318.15 K )

Next, we account for the volume change. If the volume increases by 5%, the new volume can be represented as:

• ( V' = V(1 + 0.05) = 1.05V )

Using the combined gas law, which compares the before and after states of the gas, we can express the relationship as follows, assuming the amount of gas remains constant (( n ) and ( R ) do not change):

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