# Pressure Cooker at High Altitudes and Low Altitudes

Also, I have some questions regarding boiling point and vapour pressure.

High Altitude Cooking

At high altitudes, the atmospheric pressure is lower than that at sea level, so the boiling point at high altitudes is quite low, which means water boils very fast and at low temperatures. The food inside it does not get enough heat to get cooked and thus food is difficult to cook at high altitudes.

Using a pressure cooker at such conditions helps increase the boiling time as the pressure inside the pressure cooker increases due to the vapour produced inside it. The boiling point increases and thus the time taken to reach the temperature increase and the cooking is better because the food is getting heat for a long period of time.

At Low Altitudes

The boiling point of liquid at low altitudes is more than that at high altitudes, so we do not have to worry much about less time being available for cooking the food. In fact, we try to decrease the cooking time in order to get food cooked faster. Even less amount of water can produce a good vapour pressure and get equal to the pressure produced inside the cooker. But less amount of water takes a lesser time to reach a particular temperature than more amount of water ( as $Q=mc{\delta}t$ ) and thus lesser the mass, lesser the time to get the required heat, hence faster the cooking.

Questions

1. Have I understood this perfectly or is there something more to it?

2. Does the vapour pressure of the water inside the cooker have to become equal to the vapour pressure produced due to itself in order to boil?

3. How does pressure cooker increase time for cooking at high altitudes and decrease time for cooking at low altitudes being basically the same thing?

4. The Critical temperature is the temperature at which gas just becomes liquid. The boiling point is the temperature at which all the bulk of the liquid starts turning into gas.

How are Critical and Boiling Points different?
How are they similar?
Is there any mathematical relation between them?

Edit - As 1e9dB's answer points out I made a huge mistake in this answer. The inside pressure of the pressure cooker is ambient pressure plus the extra pressure of the valve. The pressure cooker does not cook at an absolute pressure independent of altitude.

You have it all backwards. The pressure cooker allows the pressure inside the cooker to be above the sea-level atmospheric pressure which also increases temperature inside the cooker and thus decreases cooking time. So the critical factor is the increase of the boiling temperature of water as a function of the pressure inside the cooker.

The pressure cooker raises the pressure inside the cooker to the same absolute pressure, regardless of the altitude at which the cooking is being done. A typical value for the internal pressure would be about 2 atmospheres absolute which makes the internal cooking temperature about 120 °C. (The steam is pushing against the pressure regulator (weight) to escape, not the outside atmosphere. It is like the safety valve on an old steam locomotive that keeps the pressure at a certain level so that the pot doesn't blow up.)

The inside temperature of a pressure cooker when steaming (120 °C) is way below the critical temperature of water (about 374 °C) so that factor doesn't enter into the cooking time at all.

• Increase the pressure (of the surrounding) above water increases its boiling point. Water will boil at a higher temperature when the pressure above it is higher. If we consider the vapour pressure (of the water), if it is high, boiling temperature will be less since it will easily be equal to the pressure of the surroundings. This is what I meant. Though I never considered the weight of the regulator, which I'm really glad you made me aware about. How about 'increase of cooking time' for high altitudes? – Quark2 Mar 16 '16 at 2:54
• Altitude doesn't matter!! The pressure regulator sets an absolute pressure, not a pressure relative to current atmospheric pressure. So cooking time at sea-level and 10,000 feet would be the same. – MaxW Mar 16 '16 at 3:20
• en.wikipedia.org/wiki/High-altitude_cooking This means time at high altitudes with cooker is increased relative to cooking time at high altitudes without the cooker? – Quark2 Mar 16 '16 at 3:26
• You have it backwards. Let's say that I'm trying to boil some carrots. By putting them in the pressure cooker the absolute internal pressure goes to about 2 atmospheres and the temperature inside the pot goes to 120 °C - regardless of altitude! Water in an open pot at sea-level boils at 100 °C. At 10,000 feet water in an open pot boils at about 90 °C. So a pressure cooker always cooks faster. en.wikipedia.org/wiki/… – MaxW Mar 16 '16 at 3:37
• Then why the f is it said that they increase cooking time at high altitudes? ;-; – Quark2 Mar 16 '16 at 14:49

MaxW has it right except for one thing - the pressure inside the cooker does in fact does depend on altitude. For example, a cooker that will reach 15 psi at sea level will only reach about 12.5 psi in Denver.

Although it is true that the pressure is regulated by a weight which closes off a small hole, and the weight is constant regardless of altitude, remember that the ambient pressure outside the cooker is also imparting a downward force on the weight that is in opposition to the internal pressure that is imparting an upward force. At a higher altitude the internal pressure can't rise quite as much before it overcomes the lower external pressure in order to raise the weight. The result is that the internal pressure is lower by exactly the same amount as the ambient pressure difference due to altitude. That means that the boiling point inside the cooker is somewhat lower at higher altitude, although still higher than it would be outside of a pressure cooker.

Thus at higher altitude you need to increase the cooking time: Pressure Cooker PSI FAQ

• You're right, I blew it. Thanks for the correction. – MaxW Feb 2 '17 at 17:57
• Or you have to adjust the valve. I've seen pressure cookers (with a spring-loaded) valve where you can adjust the valve. Of course, the cookers has to be able to withstand a higher pressure difference if the outside pressure is lower. – Karsten Theis Mar 23 at 21:26

Some qualifications and clarifications:

1. Altitude affects average air pressure, it's quite possible for pressure to be higher than 1 bar (101 kPa) at 1 km above sea level.

2. You should be careful to clearly state what the heat flow is.

In general "heat" is a vague term which is often used to describe energy or the flow of energy. The energy required to increase the temperature of a substance depends on the mass of the substance. The rate of temperature increase depends on the heat flow (as well as the mass and other things (such as heat loss)). Assuming the same heat flow, on average a given mass of water will boil sooner (and at lower temperature) at higher altitude.

Most food cooks faster at higher temperature. So, low altitude cooking can be faster if the limiting variable is the boiling of water. Likewise, high altitude cooking will be slower if the boiling of the water is the limiting variable. This will have little to do with frying an egg or roasting meat.

Your question mixes (confuses?) time and temperature. In an open container, a given amount of water will boil quicker at high altitude (on average, with a fixed rate of energy input). The temperature rise will be the same as at low altitude, until the boiling point is reached. At the boiling point (which will be lower at higher altitude (on average)) the temperature of the liquid becomes almost constant until (almost) all of the water has boiled away. IF this temperature is the temperature the food is cooked at, then higher altitude means slower cooking.

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The critical point of a substance Tc, is the temperature and pressure (Pc) at the "end" of the vapor-liquid curve. It is the temperature above which no liquid phase can exist, regardless of pressure. (It is the highest pressure at which both liquid and gas can co-exist.) I think of it as the temperature at which (and above which) the liquid and gas are indistinguishable.

The Wikipedia article has a diagram showing a 'typical' phase diagram. [see Critical point (thermodynamics)]. That diagram shows many different regions. If you count carefully, and include the dashed lines, you can count at least 11 different areas. The major problem with this is that the dashed lines don't represent real phases, and also the names given in that diagram are arbitrary. For instance, there's no technical difference between vapor and gas. Similarly, liquid phase and compressible liquid aren't inherently different.

A gas above Tc is indeed "supercritical", by definition, however. As temperature is increased towards Tc, the properties of the liquid phase converge towards the equivalent properties of the gas (vapor). Keep in mind that when speaking of these phase diagrams, we are speaking of systems at equilibrium. Each of the two solid lines represent the points of P and T at which two phases can co-exist at equilibrium. The triple point, when it exists for a substance, is the point at which all three phases can co-exist (and shouldn't be confused with Tc).

Of course, in the real world, I'm sitting here typing with a glass of liquid water, ice, which no doubt has water vapor over it. However, if I were to wait long enough, the ice would melt, and I'd be left with liquid and vapor (gas), and if I were to wait a really really long time, the liquid would all evaporate (unless I sealed the glass). So, the real world only works "near" equilibrium, rarely exactly at it.

The phase diagram works by describing which phases exist at a given T and P. It also enables you to predict how much increase (or decrease) in P or T is necessary to move the system to a different region in the phase space. I believe it is most useful to think of Tc as the point at which there is 'no difference' between gas and liquid, rather than the point at which liquid "just becomes" gas. It is incorrect, imho, to think of a supercritical gas as a liquid, but certainly it has some properties (depending on pressure) which are similar to ones we associate with liquids.

• This answer would be greatly improved by paragraphs. At the moment I really don't want to read it because it is just a wall of text. – bon Feb 2 '17 at 20:19
• Interesting comment about the weather. So making pasting will take longer when you are in the eye of the storm... – Karsten Theis Mar 23 at 21:27