At depths greater than 2 meters in Kansas, the wintertime soil temperature is ap

Question

At depths greater than 2 meters in Kansas, the wintertime soil temperature is approximately 15 degrees C. A farmer heats his house with a heat pump using R134a, generating a temperature of 32 deg C at the exit of the compressor. The compressor entrance is saturated vapor at 5 bar, and the compressor has an isentropic efficiency of 0.8. The evaporator is buried at a depth of 2 meters. The condenser exit is saturated liquid, and a throttling valve is used between this and the evaporator. Determine the coefficient of performance.

Explanation / Answer

A typical value would be about 30 degrees Centigrade per kilometer Ground temperatures At depths below four feet, ground temperature stays a constant 50 to 55 degrees Fahrenheit year-round." The main point about temparatures below ground is that they are relatively stable or constant compared to the daily and seasonal variations of above ground temperatures because of the insulating effect of the ground itself. (Very slow to warm up and very slow to cool down.) The deeper you go, the further from the surface, the more constant the temperature compared to the surface air variation. Air heats up and cools down quickly compared to bodies of water and soil and rock heats and cools slowest of the 3. At greater depths however temperatures, while stable, gradually increase and at the great depths some of our deep mines and drill holes are reaching the temperatures considerably above 50-55 as we get closer to the molten inner core of the planet. The insulating effect of the ground contributes to making the air in working mines very hot because the heat generated in the mining activities does not dissipate very fast from the mine air into the surrounding rock and so ventilation is required to remove the hot air as well as maintaining oxygen levels. Apparently 50-55 Fahrenheit at about 4 feet is considered average, however over sufficient time periods (years) the temperature can settle at lower (or higher) temperatures. "Permafrost" which apparently covers about 20% of the earths surface is soil at or below freezing and over sufficient time periods can extend to hundreds of metres below the surface. I nearly forgot the water temperature in the pipes. Whatever the temperature of the water at it's starting point (river, water tank, dam or reservoir) the longer it is in the pipes under the ground the closer the temperature will become to the temperature of the surrounding soil. If the soil temperature is 50-55 and the water temperature at it's source starts below 50-55 it will tend to absorb heat from the surrounding soil and increase towards 50-55. If it starts above 50-55 it will loose heat and tend to decrease towards 50-55.Of course, it is very hot at the center of the earth, so there is a constant flow of heat to the surface. This creates a thermal gradient that depends on the thermal conductivity of the bedrock (how good an insulator it is). A typical value would be about 30 degrees Centigrade per kilometer, so if you are less the 10 meters below the surface, the contribution from this would be only a fraction of a degree. If you several kilometers down at the bottom of a deep mine, it would be very hot!

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