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

Answer:

T₂ =  280.17 K

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:

$\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}$

Since, the volume is constant.

Therefore,

$V_{1} = V_{2} = V\\\\\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}\\\\T_{2} = \frac{T_{1}P_{2}}{P_{1}}$

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,

$T_{2} = \frac{(270.734\ K)(470.361\ KPa)}{454.518\ KPa}$

T₂ =  280.17 K