The total pressure in a 11.3 L automobile tire is 44 psi at 11°C. By how much does the pressure in the tire rise if it warms to a temperature of 29°C and the volume remains at 11.3 L?
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P1/T1 = P2/T2
T1 and T2 must be in Kelvin.
To calculate the change in pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the temperatures from Celsius to Kelvin:
Initial temperature = 11°C + 273.15 = 284.15 K
Final temperature = 29°C + 273.15 = 302.15 K
Now, let's solve for the number of moles using the initial pressure and temperature. We'll use the ideal gas law equation and rearrange it to solve for n:
n = PV / RT
The values we have are:
P (initial pressure) = 44 psi
V (volume) = 11.3 L
R = 0.0821 (ideal gas constant, in units of L.atm/(mol.K))
T (initial temperature, in Kelvin) = 284.15 K
Now, plug these values into the equation to calculate the initial number of moles.
n_initial = (44 psi * 11.3 L) / (0.0821 L.atm/(mol.K) * 284.15 K)
Next, we'll use the same equation to calculate the final number of moles, but using the final temperature.
T (final temperature, in Kelvin) = 302.15 K
n_final = (P (final pressure) * V) / (R * T (final temperature))
Since we want to find the change in pressure, we can rearrange the equation to solve for P (final pressure):
P (final pressure) = (n_final * R * T (final temperature)) / V
Given that the volume remains constant at 11.3 L, we can substitute this value into the equation:
P (final pressure) = (n_final * R * T (final temperature)) / 11.3 L
Finally, calculate the change in pressure:
Change in Pressure = P (final pressure) - P (initial pressure)
This will give you the change in pressure when the tire warms to a temperature of 29°C while keeping the volume constant at 11.3 L.