Pressure Cookers at Altitude

Water boils at 212 deg F at sea level, of course, but the boiling temperature of pure water is a pretty strong function of the ambient pressure.   This figure shows the boiling temperature of water at different pressures.  Atmospheric pressure at sea level is around 14.7 psi, and that point is marked on the figure with a red circle. The standard operating pressure for pressure cookers is 15 lbs which means 15 psi above atmospheric pressure.  That point is marked with a green triangle in the figure.  You can see that the boiling temperature for water is around 250 deg F inside a pressure cooker operating at sea level.

How big is the heat flow?

Sometimes it is useful to have a ballpark idea of the size of a heat flow before even starting a more detailed heat transfer analysis.  It is also kind of fun to have a rough idea of the magnitude of different heat flows. To those ends, we present this figure:

Freezing water on a warm night

Everybody knows that water freezes at 32 deg F. 

Then how come frost (which is just ice that has come from the water vapor in the air) can sometimes be seen in the morning on nights when the temperature never got below 32 deg F?  

 Similarly, backpackers and desert dwellers occasionally report a film of ice on a puddle or bucket of water on not-quite-freezing nights.

The answer has to do with the nature of heat transfer.  Heat can move by conduction (movement through a solid, or a fluid at rest) by convection (movement between a solid and a flowing fluid) or by radiation (direct exchange of energy via electromagnetic waves).  The temperature of a surface depends on the temperatures of the surroundings plus the effects of all three modes of heat transfer.

From the ground...down (part 3)

Some people might think that we’ve already talked about this topic enough, but we know better. 

In the last two posts, we talked about how temperature fluctuations at the surface of the ground might affect the underground temperature, and specifically, how deeply those fluctuations might penetrate.

So, now imagine that there might be an application where it wasn’t the surface temperature nor the ground temperature that mattered, but the difference between the two.   (This actually is important for certain applications that propose to use that temperature difference to generate small amounts of electricity).

From the ground...down (part 2)

Last post we talked about the idea of a “penetration depth” to describe how deeply a fluctuating surface temperature might affect the temperature of the ground below.  

 Before we go on to talk more about the ground, we should point out that that kind of calculation isn’t limited to just temperature distribution in the ground.  It can be used to approximate the penetration depth of many situations where the surface temperature fluctuates periodically.  For example, if you wanted to estimate how deeply the temperature fluctuations penetrate into the wall of an engine cylinder, you might use properties for steel (α =17.7 mm^2/s) and the frequency of the periodic temperature variation of the cylinder (if the engine was running at 2000 rpm, you’d have 1000 temperature cycles per minute, or a frequency of 105 rad/s).  With those numbers, and using our definition of 2.2% fluctuation for the penetration from the last post, you could calculate a penetration depth of 2.2 mm. 

From the ground...down

If you’ve ever lived in a house with a basement, or spent time in a cave, you are probably aware that the temperature underground remains fairly constant regardless of what the air temperature is doing.  Many times the basement is the warmest part of the house in the winter, and the coolest in the summer.  Old time root cellars took advantage of this uniform temperature before air conditioners and central heat were common. 

  

Obviously, fluctuations in the air temperature will penetrate some distance into the ground.  How deep will they go?  While this question is fascinating all by itself, it has some practical implications, too.

Thermal Explosions

While the term thermal explosion sounds very dramatic, it really just refers to a thermal event where the heat release (or absorption) occurs over a time period that is very small relative to the time scale of interest, and in a volume that is negligibly small compared to the surroundings in which the temperature distribution is to be calculated.  So, for example, the heat released by the combustion of  blasting powder in a small hole (time scale of milli-seconds) could be analyzed as a thermal explosion if the time scale of interest was on the order of seconds.  Also the decay heat generated by a pocket of radioactive rock (say, over 100 years) could be analyzed as a thermal explosion if the period of interest were, say, 10,000 years.