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

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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): \[ \frac{P_1

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):

[

\frac{P_1

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