Thank you for visiting A car tire has a volume of 0 0150 cubic meters on a cold day at a temperature of 5 0 C and an atmospheric. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The new gauge pressure of the car tire can be calculated using the combined gas law by converting all pressures to absolute pressures, temperatures to Kelvin, and then solving for the final pressure. Subtracting the atmospheric pressure from the final absolute pressure yields the final gauge pressure.
Explanation:
The question is asking to calculate the new gauge pressure of a car tire after it has been driven and has experienced a change in temperature and volume. To solve this, we can use the combined gas law, which is an amalgamation of Boyle's, Charles's and Gay-Lussac's laws, and it holds when the amount of gas is constant, as it is in this tire problem. The combined gas law is stated as (P1 * V1) / T1 = (P2 * V2) / T2, where P is pressure, V is volume, and T is absolute temperature (in Kelvin). The gauge pressure is the pressure above atmospheric pressure, so we will need to convert our pressures to absolute pressures by adding atmospheric pressure to gauge pressures (in the same units), and we'll need to convert Celsius temperatures to Kelvins by adding 273.15.
Converting the initial and final temperatures to Kelvin gives T1 = 5.0 °C + 273.15 = 278.15 K and T2 = 45.0 °C + 273.15 = 318.15 K. The initial gauge pressure is 1.70 atm and atmospheric pressure is 1.02 atm, so the absolute initial pressure P1 is 1.70 atm + 1.02 atm = 2.72 atm. We can convert this into Pa (Pascals) if needed, using the conversion factor 1 atm = 101325 Pa. The volume initially is 0.0150 m³ and finally 0.0159 m³.
Applying the combined gas law to solve for P2 (the final absolute pressure), we get:
P2 = (P1 * V1 * T2) / (V2 * T1)
Using the above values in the formula, the final absolute pressure in atm can be found. To determine the final gauge pressure, we must then subtract the atmospheric pressure from the absolute final pressure.
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Rewritten by : Jeany
