Question

The tire is inflated (while cold) to a volume of 11.8 L and a gauge pressure of 36.0 psi (Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi.) at a temperature of 12.0 ∘C. While driving on a hot day, the tire warms to 65.0 ∘C and its volume expands to 12.2 L. What is the total pressure (gauge pressure + atmospheric pressure) in the tire after warming on a hot day?

Answer 1

To calculate the total pressure in the tire after warming on a hot day, we can use the combined gas law equation. The total pressure in the tire after warming is 53.51 psi.

Step-by-step explanation:

To calculate the total pressure in the tire after warming on a hot day, we need to consider the change in temperature and its effect on the volume of the gas. We can use the combined gas law equation, which states that the product of pressure and volume is directly proportional to the product of temperature and the ideal gas constant.

1. Convert the initial and final temperatures to Kelvin: 12.0 °C + 273.15 = 285.15 K and 65.0 °C + 273.15 = 338.15 K.
2. Use the combined gas law to calculate the initial pressure: P1 * V1 / T1 = P2 * V2 / T2
3. Plug in the given values: 36.0 psi * 11.8 L / 285.15 K = P2 * 12.2 L / 338.15 K
4. Rearrange the equation to solve for P2: P2 = (36.0 psi * 11.8 L * 338.15 K) / (285.15 K * 12.2 L)
5. Calculate P2: P2 = 38.81 psi
6. Add the atmospheric pressure of 14.7 psi to get the total pressure: 38.81 psi + 14.7 psi = 53.51 psi

Answer 2

The total pressure is 58.2 atm

Step-by-step explanation:

Step 1: Data given

The tire is inflated to a volume of 11.8 L and a gauge pressure of 36.0 psi

Atmospheric pressure is 14.7 psi, at a temperature of 12.0 °C

When the tire warms to 65.0 °C, it's volume expands to 12.2 L

Step 2: Calculate total pressure

Gauge pressure = total pressure – atmospheric pressure

Total pressure = gauge pressure + atmospheric pressure

Total pressure in 11.8 liter volume = 36.0 atm + 14.7 atm = 50.7 atm

Step 3: Calculate pressure after temperature rise

Temperature = 12°C + 273 = 285 K

The tire warms to 65.0 ∘C = 273 + 65 = 338 K

P1V1/T1 = P2V2/T2

50.7 atm*(11.8 liters)/ 285 K = P2(12.2 liters)/338 K

P2 = 50.7(11.8)*(338) / 285*(12.2)

P2 = 58.2 atm

Total pressure = 58.2 atm

Step 4: Calculate gauge pressure

Gauge pressure = 58.2 atm – 14.7 atm = 43.5 atm

The total pressure is 58.2 atm