At the start of a road trip, the pressure of the air in a car tire is 276kPa and the temperature is 12.0 degrees Celsius. After driving for some time the pressure in the tire is now 303kPa.
Assuming that the volume of the air inside the tire remains constant, determine the new temperature?
(assume an ideal gas law)
been there ,done that
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To determine the new temperature, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of the gas,
R is the ideal gas constant, and
T is the temperature of the gas.
In this case, since the volume of air inside the tire remains constant, we can rewrite the equation as:
P1/T1 = P2/T2
Where:
P1 is the initial pressure of the air in the tire,
T1 is the initial temperature of the air in the tire,
P2 is the final pressure of the air in the tire, and
T2 is the final temperature of the air in the tire.
Given:
P1 = 276 kPa,
T1 = 12.0 degrees Celsius (convert to Kelvin by adding 273.15),
P2 = 303 kPa.
Let's solve for T2:
276 kPa / (12.0 + 273.15 K) = 303 kPa / T2
To isolate T2, rearrange the equation:
T2 = (303 kPa) * (12.0 + 273.15 K) / 276 kPa
Now, calculate the value of T2:
T2 ≈ 288.32 K
So, the new temperature inside the tire after driving is approximately 288.32 Kelvin.