A car tyre has a volume of 10 L when inflated. The tyre is inflated to a pressure of 3 atm at 17°C with air. Due to driving, the temperature of the tyre increases to 47°C.
a) what would be the pressure at this temperature?
b) how many litres of air measured at 47°C and pressure of 1 atm should be let out to restore the tyre to 3 atm at 47°C?
I am too, but try this.
PV = nRT and plug in 3.31 atm, 10L, 320 K, and calculate n. That will be the number of moles at 290K as well as at 320 K. Then redo PV = nRT using 320K, 3 atm, then subtract moles at 3.31 atm from moles at 3 atm. That will be the moles that must be released. Then PV = nRT and plug in the new conditions for air to ber released. If I didn't goof the volume to be released is about 3 L *(@ 47 C and 1 atm P).
a.
(P1/T1) = (P2/T2)
b.
(P1V1/T1)= (P2V2/T2)
Yea it works. we get 3.1 litre. thanks a lot..
To answer these questions, we can use the ideal gas law, which states:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles of gas
R is the ideal gas constant
T is the temperature in Kelvin
First, let's convert the temperatures from Celsius to Kelvin:
17°C + 273 = 290 K
47°C + 273 = 320 K
a) To find the pressure at a temperature of 47°C, we can use the combined gas law, which is a rearrangement of the ideal gas law:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = 3 atm (initial pressure)
V1 = 10 L (initial volume)
T1 = 290 K (initial temperature)
T2 = 320 K (final temperature)
Rearranging the equation:
P2 = (P1 * V1 * T2) / (V2 * T1)
Plugging in the values:
P2 = (3 atm * 10 L * 320 K) / (10 L * 290 K)
P2 = 3.45 atm
Therefore, the pressure at a temperature of 47°C would be approximately 3.45 atm.
b) To find out how many liters of air should be let out to restore the tire to 3 atm at 47°C, we need to calculate the new volume using the ideal gas law.
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = 3 atm (initial pressure)
V1 = 10 L (initial volume)
T1 = 320 K (final temperature)
P2 = 1 atm (new pressure)
T2 = 320 K (final temperature)
Rearranging the equation to solve for V2 (new volume):
V2 = (P2 * V1 * T1) / (P1 * T2)
Plugging in the values:
V2 = (1 atm * 10 L * 320 K) / (3 atm * 320 K)
V2 = 3.33 L
To restore the tire to 3 atm at 47°C, approximately 3.33 liters of air should be let out.
Please note that these calculations assume that the amount of gas inside the tire remains constant throughout the process. Additionally, it's important to exercise caution and follow proper safety procedures when dealing with tire pressure adjustments.