An aerosol can is empty, except for the propellant gas which exerts a pressure of 1.20 atm at 21 °C. If the can is thrown into a fire and heated to a temperature of 565 °C, what will be the pressure inside the hot can?
Well, I hope nobody throws cans into fires, but let's solve this problem with a touch of humor!
So, you have an empty aerosol can that's about to go on a hot adventure. First of all, don't worry – it won't explode like a fireworks display at a clown convention.
Now, as the can hits the fire, things will start to heat up – more than a hotdog at a barbecue. With that increase in temperature, the propellant gas inside the can will also warm up faster than a cheetah chasing a pogo stick.
To find the pressure inside the can at the higher temperature, we can use the ideal gas law, which is as reliable as a trusty rubber chicken:
PV = nRT
In this case, we have some values to consider. Let's heat things up with numbers:
Initial pressure (P1) = 1.20 atm
Initial temperature (T1) = 21 °C + 273.15 (converted to Kelvin)
Final temperature (T2) = 565 °C + 273.15 (also converted to Kelvin)
Now, since the can is empty except for the gas, we don't need to worry about the number of moles (n) – there are no clowns huffing helium here.
So, using the ideal gas law equation, we can rewrite it to find the final pressure (P2) like this:
P1/T1 = P2/T2
Plugging in the numbers, we get:
1.20 atm / (21 °C + 273.15)K = P2 / (565 °C + 273.15)K
And after multiplying and rearranging, we find:
P2 = 1.20 atm × [(565 °C + 273.15)K / (21 °C + 273.15)K]
So, calculate those numbers like a mathemagician, and you'll discover the pressure inside the toasty can.
Just remember, it's all in good fun, so please don't throw any cans into fires – let them live a peaceful life full of hairspray and bug repellent!
To find the pressure inside the hot can, 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, we need to convert the temperatures from Celsius to Kelvin:
Initial temperature: 21 °C + 273.15 = 294.15 Kelvin
Final temperature: 565 °C + 273.15 = 838.15 Kelvin
Next, let's find the number of moles of gas present in the can:
Since the can is empty except for the propellant gas, there are no other gases present. Therefore, the number of moles of gas (n) is zero.
Now, we can set up the equation using the initial and final conditions:
P1V1 = nRT1
P2V2 = nRT2
Since the volume (V) is constant in this case, we can cancel it out:
P1 = nRT1
P2 = nRT2
Substituting the values we know:
P1 = 1.20 atm
T1 = 294.15 K
T2 = 838.15 K
P2 = nRT2
Now we can calculate the pressure inside the hot can using the ratio of temperatures:
P2 = P1 * (T2 / T1)
P2 = 1.20 atm * (838.15 K / 294.15 K)
P2 = 3.42 atm
Therefore, the pressure inside the hot can will be approximately 3.42 atm.
To determine the pressure inside the hot can, we can use the ideal gas law equation:
PV = nRT
Where:
P represents pressure
V represents volume
n represents the number of moles of gas
R represents the ideal gas constant
T represents temperature in kelvin
To solve this problem, we need to convert the given temperatures from Celsius to Kelvin. The conversion formula is:
T(Kelvin) = T(Celsius) + 273.15
Let's convert the temperatures:
Initial temperature: 21 °C
T1(Kelvin) = 21 + 273.15 = 294.15 K
Final temperature: 565 °C
T2(Kelvin) = 565 + 273.15 = 838.15 K
Next, we can rearrange the ideal gas law equation to solve for the final pressure (P2):
P2 = (P1 * V1 * T2) / (V2 * T1)
Since the can is empty except for the propellant gas, we can assume that the volume (V) remains constant, so V2 = V1.
Now we can substitute the known values into the equation:
P1 = 1.20 atm (initial pressure, given)
V1 = V2 (the volume is constant)
T1 = 294.15 K (initial temperature in Kelvin)
T2 = 838.15 K (final temperature in Kelvin)
P2 = (1.20 atm * V1 * 838.15 K) / (V1 * 294.15 K)
We can cancel out the volume (V1) since it appears in both the numerator and denominator:
P2 = (1.20 atm * 838.15 K) / 294.15 K
Finally, we can calculate the pressure inside the hot can:
P2 = 3.415 atm
Therefore, the pressure inside the hot can would be approximately 3.415 atm.
(P1/T1) = (P2/T2)
Remember T must be in kelvin.