Pressure in a Cooker at 390.2 K and 6 L Volume with 27 g Water

In summary: Since 390.2 K=117.2 degrees Celsius, the problem likely assumes that all the water is evaporated in the cooker. You have the equation PV=nRT, which can be rewritten as P=(nRT)/V. For n, you need to convert 27 g water to moles of water.The pressure (atm) in the cooker is 144 psi. The quality of the water is 77.25% vapor and 22.75% liquid.
  • #1
gwiber
5
0
1. A pressure cooker with a volume of 6 L is filled with 27 grams of water and heated to 390.2 K. What is the pressure (atm) in the cooker



2. 3) PV = nRT



3. P(6)=27*0.082*390.2
P=144
 
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  • #2
gwiber said:
1. A pressure cooker with a volume of 6 L is filled with 27 grams of water and heated to 390.2 K. What is the pressure (atm) in the cooker

2. 3) PV = nRT

3. P(6)=27*0.082*390.2
P=144


At these conditions water is not an ideal gas. It is a saturated mixture of liquid and vapor. You need to look up the saturation pressure that goes with that temperature, and also confirm that the specific volume falls between vf and vg.

BBB
 
  • #3
I think that the problem is probably asking for a much simpler approach. Since 390.2 K=117.2 degrees Celsius, the problem likely assumes that all the water is evaporated in the cooker. You have the equation PV=nRT, which can be rewritten as P=(nRT)/V. For n, you need to convert 27 g water to moles of water.
 
  • #4
ptolema said:
I think that the problem is probably asking for a much simpler approach. Since 390.2 K=117.2 degrees Celsius, the problem likely assumes that all the water is evaporated in the cooker. You have the equation PV=nRT, which can be rewritten as P=(nRT)/V. For n, you need to convert 27 g water to moles of water.

No, that is not correct. Water at these conditions is a mixture of saturated liquid and vapor and the ideal gas law does not apply. You are trying to reason from the boiling point at atmospheric pressure, not understanding that the pressure inside the fixed-volume cooker is considerably higher than atmospheric and has a much higher boiling point (for the given specific volume, somewhere around 170-175 deg C).

Two thermodynamic parameters are given: the temperature T=390.2 K and the specific volume = 0.006/0.027 m3/kg = 0.222 m3/kg. This is enough to determine the state completely. In particular, it is not hard to compute that the quality is 0.22745, i.e. the mixture is 22.75% liquid and 77.25% vapor.

So to solve the problem correctly, the OP needs to find the saturation pressure and verify that the quality is between 0% and 100%.

BBB
 
  • #5
.36 atm


I would like to clarify that the equation used to calculate pressure in this scenario is the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. Therefore, the correct calculation for pressure in the cooker would be P = (27 g/18.02 g/mol)(0.082 L atm/mol K)(390.2 K)/(6 L) = 144.36 atm. This pressure value is within the range of typical pressure used in pressure cookers, which is usually between 15-20 psi or 1.03-1.38 atm. It is also important to note that this calculation assumes ideal gas behavior, which may not always be the case in real-world scenarios.
 

1. What is a pressure cooker?

A pressure cooker is a kitchen appliance that uses steam pressure to cook food quickly. It typically consists of a pot with a locking lid and a valve that controls the pressure inside the pot.

2. How does a pressure cooker work?

A pressure cooker works by trapping steam inside the pot, which builds up pressure and increases the boiling point of water. This higher temperature and pressure cook food faster than traditional methods.

3. What are the benefits of using a pressure cooker?

Using a pressure cooker can save time and energy, as well as retain more nutrients and flavors in food. It can also tenderize tough meats and cook foods that would normally take a long time, such as dried beans, much faster.

4. Is it safe to use a pressure cooker?

Yes, pressure cookers are generally safe to use as long as they are used properly and according to the manufacturer's instructions. The lid should always be locked in place before the pressure builds up, and the pressure should be released carefully after cooking.

5. How do I know when it's safe to open a pressure cooker?

Pressure cookers typically have safety mechanisms in place that prevent the lid from being opened until the pressure inside has been fully released. It is important to follow the instructions for releasing pressure and to never force the lid open before it is safe to do so.

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