Solar Heat Engines

Solar Heat

Solar Power—Radiation from the sun received on Earth

Here is some basic information for those interested in converting solar radiation into power. At the average earth-sun distance of 92.9 million miles the solar radiation intensity is:

435 BTU/(ft²-hr) or 1370 watts/meter².  

After going through the atmosphere and reaching the ground the values drop to:

340 BTU/(ft²-hr) or 1070 W/m². 

The above value is what you have to work with at noon on a clear day at the equator. As you depart from those conditions the values decrease. A good ballpark value to use for 40 degrees North latitude appears to be around:

300 BTU/(ft²-hr) or 944 W/m². 

Just so you know there is more to learn about solar radiation, there is the total radiation which is the sum of direct normal radiation (sunlight), diffuse or sky radiation (when you stand in the shade it isn’t dark and your solar calculator still works), and reflected solar radiation (you probably noticed it’s warmer in the sun by the south side of a building).

The above numbers will get you started if you know what to do with them. I’ll talk about heating things up with solar power on a future post so you can figure how much heat you need to change the temperature of things like air, water, or a piece of metal.  

By the way, typical solar cells have about 10% conversion efficiency so you get roughly 94 W/m² out of them. State-of-the-art solar cells are approaching 15-20% efficiency.

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How much heat to raise the temperature?

Everyone knows it takes heat to raise the temperature of something, whether it’s the air in your house or a kettle on the stove. If you want to design heat engines or use solar power to elevate the temperature of something, it helps if you can determine how much heat you need.

To begin with I’ll skip phase changes and just look at heating things that stay in the same phase—solid, liquid, or gas.

The basic equation is:

Q=mc(deltaT)

 where:

Q = heat (units: cal, kcal, Joules, ft-lb, Btu, or kWhr)

m= mass (units: kg or lb)

c= specific heat for the particular material and temperature (units:kJoules/(kg-degC) or Btu/(lb-degF)

deltaT = change in temperature (units: degC, or degF)

To use the above equation correctly you need to make sure you use consistent units.

Below is a table that contains specific heats for various materials at 20 deg C. If you need other materials you can probably find them on the web or in handbooks for engineering, physics, or chemistry. Note that the values change with temperature and may change greatly when the substance goes through a phase change. These values are also for constant pressure. If you heat or cool at constant volume there are other numbers to use and I’ll discuss that at a later date.

I’ll give a few examples:

You want to raise the temperature of 1.5 pounds of aluminum by 50 degF then you’ll need:

Q=1.5lb x 0.22 Btu/(lb-degF) x 50 degF = 16.5 Btu of heat

You want to raise the temperature of 0.1kg of air by 100 degC

Q=0.1kg x 1.02kJ/(kg-degC) x 100degC = 10.2kJ

A few useful conversions:

1kw-hr = 3412 Btu

1 kw-hr = 3600 kJ,

1Btu=1.055kJ

Sources:

Marks’ Handbook for Mechanical Engineers, tenth edition

General Physics, 1984, Giancoli, Douglas

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