Question

What final temperature (∘c) is required for the pressure inside an automobile tire to increase from 2.19 atm at 0 ∘c to 2.37 atm , assuming the volume remains constant?

Answer 1

To find the final temperature required for the pressure inside an automobile tire to increase from 2.19 atm to 2.37 atm, we can use the Ideal Gas Law equation. By plugging in the initial and final pressure values, we can solve for the final temperature, which is approximately 30.64°C.

Step-by-step explanation:

To solve this problem, we can use the Ideal Gas Law equation:

P1/T1 = P2/T2

Where P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure, and T2 is the final temperature.

In this case, we know that P1= 2.19 atm, T1= 0°C, P2= 2.37 atm, and we need to find T2.

Plugging in the values into the equation:

(2.19 atm)/(273.15 K) = (2.37 atm)/(T2 K)

Therefore, T2 = (2.37 atm x 273.15 K) / (2.19 atm) = 303.79 K.

Converting 303.79 K to °C:

T2 = 303.79 K - 273.15 = 30.64°C.

Answer 2

22.45 c
The ideal gas law is PV = nRT where P = pressure V = volume n = number of moles R = ideal gas constant T = absolute temperature Since converting from 0 centigrade to kelvin, we get an absolute temperature of 273.15 K. Because the values of P, n, and R are all remaining constant, we can simplify the equation to a simple ratio of pressure vs temperature. So P1/P2 = T1/T2 Cross multiply P1*T2 = P2*T1 And divide by P1 T2 = P2*T1/P1 Substitute the known values and calculate T2 = P2*T1/P1 T2 = 295.6006849 So the final temperature is 295.6 K, which we need to convert to C by subtracting 273.15 295.6 - 273.15 = 22.45068493 So the answer to two decimal places is 22.45âc