a bicycle is filled with air to a pressure of 6.80atm and a temperature of 19 degrees celsus. Riding the ike on asphalt on a hot day increases the temperature of the tire to 58 degrees celcius. The volume of the tire increases by 4.0%. What is the new pressure in the bicycle tire?
Note the correct spelling of celsius.
The easy way to do these is to assume an initial volume, any number that is convenient will do. Then the new volume is 0.04 x that initial volume.
{P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.
To find the new pressure in the bicycle tire, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
First, let's determine the initial volume of the tire before it expands. Given that the volume increases by 4.0%, we can calculate the initial volume using the formula:
Initial Volume = Final Volume / (1 + Volume Increase Percentage)
Let's calculate the initial volume:
Initial Volume = Final Volume / (1 + 4.0%)
Initial Volume = Final Volume / 1.04
Since we know the relationship between the initial and final volume is V_initial = V_final / 1.04, we can rewrite the ideal gas equation as:
P_initial * V_initial = nR * T_initial
Similarly, the final pressure can be written as:
P_final * V_final = nR * T_final
Dividing the two equations:
(P_initial * V_initial) / (P_final * V_final) = (T_initial) / (T_final)
Rearranging the equation to solve for the final pressure:
P_final = (P_initial * V_initial * T_final) / (V_final * T_initial)
Now, let's substitute the given values into the equation:
P_initial = 6.80 atm
T_initial = 19°C + 273.15 = 292.15 K
T_final = 58°C + 273.15 = 331.15 K
Let's assume the volume of the tire was initially 1 unit, we can then calculate the final volume as:
V_final = V_initial * (1 + Volume Increase Percentage)
V_final = 1 * (1 + 4.0%) = 1.04
Now, plugging in the values:
P_final = (6.80 atm * 1 * 331.15 K) / (1.04 * 292.15 K)
Calculating the final pressure:
P_final = 6.80 * 331.15 / (1.04 * 292.15)
P_final ≈ 7.015 atm
Therefore, the new pressure in the bicycle tire is approximately 7.015 atm.
To find the new pressure in the bicycle tire, we need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (initial and final)
V = Volume (initial and final)
n = Number of moles of gas (constant)
R = Ideal gas constant
T = Temperature (initial and final)
First, let's calculate the initial volume of the tire. Since the volume increases by 4.0%, the final volume (Vf) would be 104.0% (or 1.04) of the initial volume (Vi). Therefore,
Vf = 1.04 * Vi
Next, let's convert the initial pressure to Pascal (Pa) since the ideal gas constant (R) is usually given in terms of Pa. 1 atm = 101325 Pa. Thus,
Pi = 6.80 atm * 101325 Pa/atm
Now, let's convert the initial temperature to Kelvin (K) since the ideal gas law equation requires temperature in Kelvin. To convert Celsius to Kelvin, we add 273.15.
Ti = 19°C + 273.15 K
Finally, we can substitute all the values into the ideal gas law equation to solve for the final pressure (Pf):
Pi * Vi = Pf * Vf
Pf = (Pi * Vi) / Vf
Remember to convert Pf back to atm if desired.