If a gas in a closed container is pressurized from 12 atm to 25 atm and tis original temperature was 32 degrees C, what would the final temperature of the gas be?
Tf = 635 K
Oh, we're heating things up now! Well, when it comes to pressure and temperature, it's like playing a game of hot potato. Here's the deal: if you increase the pressure, then the temperature tends to go up as well. It's like sitting on a crowded bus – things just naturally heat up!
So, with a starting temperature of 32 degrees C and a pressure increase from 12 atm to 25 atm, we need to calculate the final temperature. And guess what? It's a toasty 635 K!
That's like turning up the oven to full blast. So, get ready to break out the sunscreen because things are about to get steamy! Enjoy the heat!
To find the final temperature (Tf) of the gas, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas (which is constant in this case since it is a closed container)
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas (in Kelvin)
First, let's convert the original temperature from degrees Celsius to Kelvin. The relationship between Celsius and Kelvin is:
T(K) = T(°C) + 273.15
So, the original temperature (T1) in Kelvin is:
T1 = 32 + 273.15
T1 = 305.15 K
We are given that the initial pressure (P1) is 12 atm and the final pressure (P2) is 25 atm.
Since the volume (V) is constant, we can rewrite the equation as:
P1/T1 = P2/T2
Substituting the known values:
12 atm / 305.15 K = 25 atm / Tf
Now we can solve for Tf:
12Tf = 25 * 305.15
Tf = (25 * 305.15) / 12
Tf ≈ 635 K
Therefore, the final temperature of the gas would be approximately 635 K.
To find the final temperature of the gas, we can use the ideal gas law formula which is given as:
PV = nRT
where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas
In this case, the volume and the number of moles of the gas are constant because the gas is in a closed container. Therefore, we can simplify the formula to:
P1/T1 = P2/T2
where:
P1 = initial pressure of the gas
T1 = initial temperature of the gas
P2 = final pressure of the gas
T2 = final temperature of the gas
Now, let's plug in the values given:
P1 = 12 atm
T1 = 32 degrees C + 273.15 (converting to Kelvin) = 305.15 K
P2 = 25 atm
We can rearrange the formula to solve for T2:
T2 = (P2 * T1) / P1
Substituting the values:
T2 = (25 * 305.15) / 12
T2 ≈ 635 K
Therefore, the final temperature of the gas would be approximately 635 K.