The car tyre contains air initially at a pressure of 195 kPa after travelling several km the temperature of the air inside a car tyre rises from 30 to 70°C if the tyre is rigid and does not expand then the new pressure inside the tyre would be 220.74 kPa.
<h3>What is pressure?</h3>
The total applied force per unit of area is known as the pressure.
The pressure depends both on externally applied force as well the area on which it is applied.
The mathematical expression for the pressure
Pressure = Force /Area
the pressure is expressed by the unit pascal or N /m²
By using the Charles law for gases which states that the volume of the gas remains constant then the pressure of the gas is directly proportional to the temperature.
As given in the problem the tyre is rigid and does not expand this means the volume of the tyre remains constant.
The mathematical expression for Charles's law is as follows
P₁/P₂ = T₁/T₂
First, we have to change the temperature from degree Celcius to the kelvin temperature scale
K = 273 + C
where k is the temperature in kelvin and the C is degrees of Celcius
Initially, the temperature was 30° C
T₁ = 273 + 30
T₁ = 303 K
Then after travelling the temperature of the air inside a car tyre rises from 30 to 70°C
T₂= 273+ 70
T₂ =343 K
The car tyre contains air initially at a pressure of 195 KPa
P₁ = 195 kPa
Lets us take the final pressure of the air would be P₂
By substituting the values in the formula
P₁/P₂ = T₁/T₂
195/P₂ = 303/343
P₂ = 220.74 kPa
Thus, the new pressure inside the tyre would be 220.74 kPa.
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