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Answer :
Final answer:
Using the Ideal Gas Law in the form P1/T1 = P2/T2, considering that the pressure in the tire was initially 210 kilopascals (kPa) at 25°C (298 K), and we want to find the pressure at 0°C (273 K), we find that the pressure would be approximately 192.6 kPa or approximately 27.95 psi when the temperature is 0°C.
Explanation:
To estimate the gauge pressure in your car tires when the temperature drops to 0°C, we can use the Ideal Gas Law, which is PV = nRT, where: P is pressure, V is volume, n is the mole of gas, R is the gas constant, and T is temperature. However, because the numbers of moles n and the volume V remains constant, we can simplify the equation to P1/T1 = P2/T2. P1 is the original pressure, T1 is the original temperature, P2 is the pressure we want to find, and T2 is the new temperature.
Given P1=210 kPa and T1=25°C (or 298 K in Kelvin), and T2=0°C (or 273 K in Kelvin), we can substitute these into P1/T1 = P2/T2 to find P2. So, P2 = P1 * T2 / T1 = 210 kPa * 273 K / 298 K = 192.6 kPa (approximately). This is around 27.95 psi.
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Rewritten by : Barada
Under the assumption that the tires do not change in volume, apply Gay-Lussac's law:
P/T = const.
P = pressure, T = temperature, the quotient of P/T must stay constant.
Initial P and T values:
P = 210kPa + 101.325kPa
P = 311.325kPa (add 101.325 to change gauge pressure to absolute pressure)
T = 25°C = 298.15K
Final P and T values:
P = ?, T = 0°C = 273.15K
Set the initial and final P/T values equal to each other and solve for the final P:
311.325/298.15 = P/273.15
P = 285.220kPa
Subtract 101.325kPa to find the final gauge pressure:
285.220kPa - 101.325kPa = 183.895271kPa
The final gauge pressure is 184kPa or 26.7psi.
