Pressure Cooker-Involving Ideal Gas law and Total Pressure

In summary, the pressure inside the container can be calculated by using the Total Pressure law and the ideal gas law. The initial pressure and temperature can be assumed to be standard conditions. By using the partial pressure of air and water, the total pressure inside the container is found to be 1869 kPa.
  • #1
tcw46
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Homework Statement


A cook puts 9.00g of water in a 2.00L pressure cooker and warms it to 500 degree celcius. What is the pressure inside the container.

Homework Equations


[tex]P_{total} = P_{1} + P_{2} +...[/tex] (eqn1)

[tex]PV = nRT[/tex] (eqn2)

[tex]\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{1}}[/tex] (eqn3)

The Attempt at a Solution


I've assumed that the initial pressure and temperature are standard conditions (101 kPa & 298k)

Using the Total Pressure law, I know that [tex]P_{i Total} = P_{atm/air} \; and \;P_{f Total} = P_{air,\, heated\, to\, 773K} + P_{Water} [/tex]

[tex]Total Volume = 2.00L = 0.00200m^3[/tex]

[tex]T_{initial} = 298K \; and \; T_{final} = 773K[/tex]

using eqn3 i found [tex]P_{air} = 261990Pa[/tex] by substituting relative values. (using P1 = 101x1^3 Pa)

at the beginning the pressure of water can be neglected, since it's a liquid.
However at 773K, i use PV=nRT to calculate the partial pressure of water.

n=9.00g/18gmol^-1 = 0.5mol T = 773K V = 0.002m^3 and R = 8.314 J mol^-1 K^-1
Partial Pressure of Water = 1606680 Pa.

Therefore total pressure = sum of the two partial pressure = 1868670 Pa or 1869 kPa.

I'm just wondering whether someone could check this over for me and give me any comments, since I'm a bit nervous about the huge answer :S

Thanks
 
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  • #2
Seems ok to me. Unless I made the same mistake you did :)
 

1. What is the Ideal Gas Law?

The Ideal Gas Law is a fundamental equation in chemistry that describes the relationship between the pressure, volume, temperature, and amount of gas in a system. It is written as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature.

2. How does a pressure cooker involve the Ideal Gas Law?

A pressure cooker involves the Ideal Gas Law because it uses the law to increase the pressure inside the cooker, which in turn increases the temperature of the water and food inside. This allows for faster cooking times and more tender results.

3. What is the total pressure in a pressure cooker?

The total pressure in a pressure cooker is equal to the sum of the atmospheric pressure and the pressure from the steam inside. This is typically around 15 psi (pounds per square inch) in a modern pressure cooker.

4. How does the Ideal Gas Law affect the cooking process in a pressure cooker?

The Ideal Gas Law affects the cooking process in a pressure cooker by increasing the pressure and temperature inside the cooker, which allows for faster cooking times and more tender results. It also helps to retain moisture in the food, resulting in juicier and more flavorful meals.

5. Are there any safety concerns when using a pressure cooker involving the Ideal Gas Law?

While pressure cookers can be safe to use when following proper instructions, there are some safety concerns to be aware of. The high pressure and temperature inside the cooker can cause steam to escape rapidly if not properly released, which can result in burns. It is important to carefully follow the manufacturer's instructions and never open the cooker until all steam has been released and the pressure has returned to normal.

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