ANSWER..........................
Answers
Given that the Pressure in the tyre is 200 kPa above the Atmospheric pressure of 100 kPa
⇒ We can notice that the Pressure Gauge is indicating the Gauge Pressure
We know that Absolute Pressure = Gauge Pressure + Atmospheric Pressure
⇒ Absolute Pressure in the tyre : P₁ = 200 + 100 = 300 kPa
At this Pressure the Temperature of the Air inside the tyre = T₁ = 25 + 273 = 298 K
After Driving on Hot roads the Temperature of the Air inside the tyre = T₂ = 50 + 273 = 323 K
Assuming the Air inside the Tyre as Ideal gas, We know that According to Ideal gas Equation : (P₁ × V₁)/T₁ = (P₂ × V₂)/T₂
As the Volume of the Tyre remains Constant : V₁ = V₂
⇒ P₁/T₁ = P₂/T₂
substituting the respective values of Pressure and Temperature we get :
⇒ 300/298 = P₂/323
⇒ P₂ = (300 × 323)/298 = 325.17 kPa
But this is the Absolute Pressure of the tyre at 50°C
⇒ Pressure Gauge reading of the tyre at 50°C = 325.17 - 100 = 225.17
The Increase in the Pressure Gauge reading = 225.17 - 200 = 25.17 kPa
The % Increase in the Pressure Gauge reading = (25.17/200) × 100 = 12.5 %