I understand there is a relationship between pressure & temperature in a sealed rigid container.
An open container is placed in a freezer at -15 degrees C then the door is opened and the cap replaced with the freezer at 1000mb what will the pressure be within the container if it is placed in a room with an ambient temperature of 40 degrees C
Thanks
Mike
Same answer as yesterday:
http://www.jiskha.com/display.cgi?id=1323068189
Thank you again DRWLS but ref my post "site not working correctly". Still cannot read the answer. Most frustrating. Can I close the adverts? Mike
Here is the same answer, again.
If you cover an open cold container after removing it from the freezer, warm air at 313 K and P = 1000 mb will come in contact with the contents, and (after sealing with a lid) chill at constant volume to 258 K.
Since P/T = constant in this case, you end up with a pressure P' that satisfies the equation
P'/258 = Po/313, where Po = 1000 mb
P' = 258/313 * 1000 = 824 mb
Note that I had to use Kelvin temperatures.
To determine the pressure within the container when it is placed in a room with an ambient temperature of 40 degrees C, we can use the ideal gas law. The ideal gas law states the relationship between pressure (P), volume (V), number of moles (n), and temperature (T) of a gas.
The ideal gas law equation is:
PV = nRT
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of the gas
- R is the ideal gas constant (8.31 J/(mol·K))
- T is the temperature of the gas in Kelvin (K)
First, let's convert the temperatures from Celsius to Kelvin.
- The temperature of the freezer (-15 degrees C) in Kelvin: T1 = -15 + 273.15 = 258.15 K
- The ambient temperature of the room (40 degrees C) in Kelvin: T2 = 40 + 273.15 = 313.15 K
Since the container is open, it is not sealed, and the pressure inside the container will equalize with the atmospheric pressure outside. The atmospheric pressure is given as 1000 millibars (mb).
Now, we have the temperatures and the atmospheric pressure, so we can solve for the pressure within the container using the ideal gas law.
P1V1/T1 = P2V2/T2
Given:
- P1 (initial pressure) = 1000 mb
- V1 (initial volume) = V2 (final volume) since the container is rigid and volume doesn't change
- T1 (initial temperature) = 258.15 K
- T2 (final temperature) = 313.15 K
Using the formula, we can now solve for P2 (final pressure):
P2 = (P1 * V1 * T2) / (V2 * T1)
Since V1 = V2 and P1 = 1000 mb, we can simplify the equation to:
P2 = (1000 mb * T2) / T1
Plugging in the values, we get:
P2 = (1000 mb * 313.15 K) / 258.15 K
Calculating this expression will give us the final pressure (P2) within the container when it is placed in the room.