Microwave oven efficiency

How efficient is a microwave oven? Does the efficiency decline as the oven ages?
Our 15-year old kitchen microwave appears to heat things slower than it did
when new, so I did an experiment to see how long it would take to heat 2 cups of water from near freezing to boiling. It took about six minutes, but, by my estimate, should have been accomplished in under one minute: (2 cups)*(2.366e-4 m^3/cup)*(1000 kg/m^3)*(1000 g/kg)* (4.186 J/g-degC)*(100 degC)*(1 sec/5400 J)*(1/0.64)W sec. The microwave is either 6500W or 5400W, depending on the voltage supplied, so I assumed the lower. 4.186 is the specific heat of water. 0.64 is Wikipedia's estimate of a typical oven efficiency (no citation given). The time would have to be increased to account for the heating of the Pyrex glass container, but glass has a specific heat about 20% that of water, so little additional energy is needed to heat the glass. Am I missing something?
Gordon
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Dear Gordon:

~ 60%.

Good question.

Seems about right with my new one.

You have built the 5400 into your formula...

Wahoo! You have three phase microwave, receiving 400-480vac 3 phase power, consuming the power of a 7.5hp motor? Better look again.
David A. Smith
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N:dlzc D:aol T:com (dlzc) wrote:

You are correct. This microwave oven is part of a combination conventional oven/microwave cooking center. The name plate is located inside the microwave but no doubt applies to the entire appliance, which is nominally a 6.5kW appliance. I eventually found in a manual that the "microwave power output" is listed as 800 watts (IEC-705 Procedure), which already has the efficiency factored in. Replacing the 5400*0.64 above with 800 changes the result to 4.1 min. If that time is increased by another 20% to account for heating the glass container, the estimated time is now about five minutes, not so far from my measured time of about six minutes.
Gordon
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Dear Gordon:
...

Klystron tubes go out of fashion, but they really don't "degrade". There is a "window" that allows the microwaves to enter the cooking chamber. Sometimes this gets occluded with debris, and this can reflect some of the energy back into the kystron. So a good thorough cleaning (with cautions) might speed things up.
David A. Smith
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On Mon, 18 Feb 2008 16:39:52 -0700, "N:dlzc D:aol T:com \(dlzc\)"

The microwave generator found in domestic microwaves is (I thought?) a magnetron. As its name implies, the magnetron features a high magnetic field across a copper block with a central hole for a cathode and peripheral holes for tuned cavities in the anode(s). The field spins the electron cloud in a rotary spoke pattern round the cathode, exciting the cavities in turn. RF is taken out though a tap in one of the cavities to a short waveguide section to a 'mode stirrer'..
Brian Whatcott Altus OK
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Dear Brian Whatcott:

...
Correct. A klystron tube receives RF from a magnetron... in radar applications. Thanks for the catch.
David A. Smith
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On Mon, 18 Feb 2008 12:35:11 -0500, "Gordon"

I have a suspicion that the heating rate of my domestic unit is not linear with target mass. Two cups seem to take more than twice as long as one cup. But I have not tested this objectively - perhaps you might though?
Brian W
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Brian Whatcott wrote:

Apparently the current standard for testing the output power of microwave ovens is the international IEC-705 test procedure. http://www.gallawa.com/microtech/output.html This procedure does what I did with the heating of water. The multiplier of 70 appearing on this web page can be verified as follows: Output Power=(4.186 watt-sec/g-degC)*(1000 g)/(63 sec.)*Tf.4T, where 4.186 is the specific heat of water, a joule is a watt-sec, and T is the temperature rise. The standard uses the multiplier 70 instead of 66.4. There is no explanation in the cited article, but perhaps the difference is intended to account for some heating of the water container, which certainly occurs.
Brian's suspicion about a dependency on mass is discussed here and referred to as "well-known" http://www.patentstorm.us/patents/5883801-description.html See the two paragraphs containing "IEC 705".
Gordon
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