Question

Before you drive to school, the pressure in your car tire is 3 atm at 20°C. At the end of the trip

to school, the pressure gauge reads 3.2 atm. What is the new temperature in Kelvin of air inside the
tire?

Answer 1

In this case, we have:
P1 = 3 atm
V1 = Unknown (volume doesn't affect temperature change in this case)
T1 = 20°C + 273.15 (to convert to Kelvin)
P2 = 3.2 atm
V2 = Unknown (volume doesn't affect temperature change in this case)
T2 = Unknown (what we need to find)

Let's plug in the values into the combined gas law equation and solve for T2:

(3 atm × V1) / (20°C + 273.15 K) = (3.2 atm × V2) / T2

Since the volume is constant in this scenario, we can simplify the equation to:

3 / (20 + 273.15) = 3.2 / T2

Now we can solve for T2 by cross-multiplying:

3 × T2 = (20 + 273.15) × 3.2

T2 = (20 + 273.15) × 3.2 / 3

Calculating the right side of the equation:

T2 = 293.15 K × 3.2 / 3

T2 ≈ 314.53 K

Therefore, the new temperature in Kelvin of the air inside the tire at the end of the trip to school is approximately 314.53 K.