At the start of a road trip, the pressure of the air in a car tyre is 276kPa and the temperature is 12.0 degrees celsius. After driving for some time the pressure in the tyre is now 303kPa.
Assuming that the volume of the air inside the tire remains constant, determine the new temperature?
(assume an ideal gas law)
P V = n R T
P/T = n R/V
so in this problem P/T is constant
12 + 273 = 285 degrees Kelvin
276/285 = 303/T
so
T =303 *(285/276) in degrees Kelvin
subtract 273 to get degrees centigrade
To determine the new temperature inside the car tire, you can use the ideal gas law equation:
PV = nRT
where:
P is the pressure of the gas (in Pascals or Pa)
V is the volume of the gas (in cubic meters or m³)
n is the number of moles of gas
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature of the gas (in Kelvin or K)
To solve for the new temperature, we can rearrange the equation as:
T = (PV) / (nR)
First, we need to convert the pressure from kilopascals (kPa) to Pascals (Pa). Since 1 kPa = 1000 Pa, the initial pressure of 276 kPa is equivalent to 276,000 Pa, and the new pressure of 303 kPa is equivalent to 303,000 Pa.
Now, we can plug in the known values into the equation. Since the volume remains constant, n and R are constants as well.
Initial pressure (P1) = 276,000 Pa
New pressure (P2) = 303,000 Pa
Initial temperature (T1) = 12.0 degrees Celsius = 12.0 + 273.15 K (converting to Kelvin)
T2 = (P2 * V) / (n * R)
However, since n, V, and R are constant, we can simplify the equation to:
T2 = (P2 * T1) / P1
Now we can substitute the values:
T2 = (303,000 * (12.0 + 273.15)) / 276,000
Calculating this will give us the new temperature inside the car tire.