Question

You start driving your car when the air temperature is 270.734 K. The air pressure in the tires is 454.518 kPa. After driving a while, the tire's air pressure increases to 470.361 kPa. What is the temperature of the tires at that point, assuming the volume remains constant

Answer 1

T₂ = 280.17 K

Step-by-step explanation:

Here, we can use the equation of state to find the final temperature of air in tires. Equation of State is written as follows:

`(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))`

Since, the volume is constant.

Therefore,

`V_(1) = V_(2) = V\\\\(P_(1))/(T_(1)) = (P_(2))/(T_(2))\\\\T_(2) = (T_(1)P_(2))/(P_(1))`

where,

T₂ = Final Temperature of Air in Tire= ?

T₁ = Initial Temperature of Air = 270.734 K

P₁ = Initial Pressure of Air = 454.518 KPa

P₂ = Final Pressure of Air = 470.361 KPa

Therefore,

`T_(2) = ((270.734\ K)(470.361\ KPa))/(454.518\ KPa)`

T₂ = 280.17 K