# The 1.676hp Microwave Saga: Part 4

As luck would have it, a friend recently replaced their microwave and lent us their old 1100W microwave for sciencing, before proper disposal.  Until now, the focus of our ongoing series on understanding the power output of a new 1250W microwave has been based on estimating the output of an 1100W microwave.  In this installment we can see how accurate those estimates were.

#### Initial observation:

Most microwave instructions are based on an 1100W (1.475hp) microwave, but many modern microwave ovens are 1250W (1.676hp), making it difficult to chose power levels that conform to the instructions.

#### Question:

Is our previous estimate, that power level P9 (9 of 10) on a 1250W microwave really output approximately 1100W, correct?  Additionally, which power level is appropriate when instructions call for 50% on an 1100W microwave?

#### Expectation:

In our previous tests, a very linear relationship between input power and the temperature change was observed.  Additionally, since the input power data made it clear when 1250W is being output and when 0W is being output, we are confident in out estimate of when the microwave was outputting nearly 1100W based on the resulting heating data.

#### Procedure:

Unlike previous trials, here we are only interested in 100% and 50% on an 1100W microwave, which are the most common power levels called for in the instructions for frozen dinners.  In previous testing on the 1250W microwave, 50% of full power fell between P4 and P5, so we restricted testing here to levels P10, P5, and P4.

1. Avoid using the microwave for several hours or days.
2. Plug the microwave into the Kill-A-Watt.
3. Measure 500g of cold tap water into microwave safe container.
4. Record the mass of the water.
5. Measure and record initial temperature of the water.
6. Point camera at Kill-A-Watt and start recording.
7. Microwave water for 120 seconds at full power.
8. Stir water with spoon to account for any uneven heating.
9. Measure and record final temperature of water.
10. Stop recording video.
11. Carefully dispose of the hot water.
12. Repeat steps 0 through 10 three times for statistical analysis.
13. Repeat steps 1 through 11 with power levels 4 and 5.

#### Data:

Below is a table of the averages (with 95% confidence intervals), for the collected data.

 Mass (g) Initial Temp. (ºC ) Final Temp. (ºC ) Change (ºC ) P10 500.23±0.17 16.30±0.45 61.30±0.23 45±0.23 P5 500.23±0.17 16.90±0.11 35.97±0.24 19.07±0.13 P4 500.17±0.66 17.70±0.20 32.37±0.17 14.67±0.07

For full power (P10) on the 1100W microwave, the 95% confidence interval is from 44.77ºC to 45.23ºC.  On the 1250W microwave, P9’s confidence interval was from 44.34ºC to 44.92ºC.  Since these overlap, we cannot reject the null hypothesis that P10 on an 1100W microwave and P9 on a 1250W microwave are the same (i.e., the difference is statistically insignificant).

For 50% of 1100W, things are a bit more complicated.  One would expect that P5 would be half of P10, however 19.07±0.13ºC is well below 22.5±0.12ºC (half of 45±0.23ºC).  The expected amount of heating for 50% of 1100W (~22.5ºC) is therefore between P5 and P4 for the 1250W model which are 25.83±1.12ºC and 17.63±1.44 respectively.

If we instead assume that the instructions mean whatever P5 on the 1100W microwave is, when they call for 50%, then 19.07±0.13ºC is the range we’re looking for.  In this case, P4 on the 1250W model (17.63±1.44) overlaps with P5 on the 1100W model.

Note: The power data is not reported here, but was collected for later analysis.

#### Conclusion:

As expected, the difference between using P9 on a 1250W microwave and P10 (full power) on a similar 1100W model is statistically insignificant (p=0.05).  The data for 50% was less conclusive, as 50% of 1100W seems to be between power levels on both the 1100W model and definitely between levels on the 1250W model.  If 50% of 1100W is within the range of P6, it is unlikely that the average user of that microwave would guess to use P6 for 50% of P10.  If however, P5 which a reasonable person would (incorrectly) assume is 50% on an 1100W model is what is intended, then the difference between P4 on the 1250W and the intended level is statistically insignificant from that power level.

In summary, when instructions based on an 1100W microwave call for 100% or 50%, power levels P9 and P4 (respectively) should be used on the new 1250W model.

#### Future Questions:

So far our examination of the 1250W microwave has focused only on how much it can heat 500g of water.  When heating actual food are the same relative levels of heating observed?  Are there any observable differences in food quality between an inverter based microwave and one that uses pulse width modulation?