A bicycle tire is filled with air to a pressure of 610 kPa at a temperature of 19 oC. Riding the bike on asphalt on a hot day increases the temperature of the tire to 58 oC. The volume of the tire increases by 4.0%. What is the new pressure in the bicycle tire?
To find the new pressure in the bicycle tire after the temperature increase and volume expansion, we can use the ideal gas law equation:
P1V1/T1 = P2V2/T2
Given:
P1 = 610 kPa (initial pressure)
T1 = 19 oC (initial temperature in Celsius)
T2 = 58 oC (final temperature in Celsius)
ΔV = 4.0% (volume expansion as a percentage)
First, we need to convert temperatures from Celsius to Kelvin:
T1 = 19 + 273 = 292 K
T2 = 58 + 273 = 331 K
Next, we need to calculate the volume change. Since the volume increases by 4.0%, the final volume will be 100% + 4.0% = 104.0% of the initial volume.
V1 = V2/1.04
Now, we can substitute the values into the ideal gas law equation:
P1V1/T1 = P2V2/T2
610 kPa * (V2/1.04) / 292 K = P2 * V2 / 331 K
By cross-multiplying and rearranging the equation, we can solve for P2:
610 kPa * (V2/1.04) * 331 K = P2 * V2 * 292 K
610 kPa * (V2 * 331 K) = P2 * V2 * (1.04 * 292 K)
201,410 V2 = 303.68 P2 * V2
Now, we can cancel out the V2 terms:
201,410 = 303.68 P2
Finally, we can solve for P2:
P2 = 201,410 / 303.68
P2 ≈ 662.68 kPa
Therefore, the new pressure in the bicycle tire after the temperature increase and volume expansion is approximately 662.68 kPa.
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 = ideal gas constant
T = temperature in Kelvin
First, let's convert the initial temperature of 19 oC to Kelvin:
T_initial = 19 oC + 273.15 = 292.15 K
Next, let's convert the final temperature of 58 oC to Kelvin:
T_final = 58 oC + 273.15 = 331.15 K
Now, since the volume increases by 4.0%, we can calculate the new volume:
V_final = V_initial + ΔV
ΔV = 4.0% * V_initial
V_final = V_initial + 0.04 * V_initial = 1.04 * V_initial
The number of moles (n) and the ideal gas constant (R) are constant in this case. So, the ideal gas law equation can be rewritten as:
P_initial * V_initial = P_final * V_final
Substituting the values that we have:
610 kPa * V_initial = P_final * (1.04 * V_initial)
Simplifying the equation:
610 kPa = P_final * 1.04
Now solve for P_final:
P_final = 610 kPa / 1.04
P_final ≈ 586.54 kPa
Therefore, the new pressure in the bicycle tire is approximately 586.54 kPa.
21
No volume is given; therefore, make up an easy one like 1 L.
Use PV = nRT and solve for n
Using n from the first calculation, use PV = nRT again using the new conditions and remember V is to be increased by 4%. Whatever value chose for V, the new V will be the old V plus 0.04 x old V.