Thursday, November 21, 2013

Home exam graded & reported + comment on question 3

I have reported all grades for all students in the course to the KTH administrators. It usually takes a few days for this info to go through KTH's administrative system and enter LADOK - but it's on it's way.

You produced a huge number of pages (that's the drawback of home exams) and it has unfortunately taken me a long time to read and grade them all. There is one remarkable thing I really do have to comment on in regards to your exams though and that is question 3A ("How many energy slaves does it take to run your TV for 8 hours?").

A substantial number of students have mixed up the units Watts (W) and Watt-hours (Wh or kWh). That's basically like mixing up speed (km/h) and distance (km).

The figures you have heard in the course (or that can find on the web) is that an energy slave can generate somewhere between 75-100 W. If you have a TV that consumes 75-100 W you will thus need one energy slave biking constantly for 8 hours to run your TV for 8 hours. If your TV consumes 150-200 W you'll need 2 energy slaves (and so on).

In real life, you might have to take into consideration that not all slave-generated energy can be perfectly transformed into electricity, that a slave might not be able to bike for 8 hours straight since he/she needs to rest now and then (and eat - which is a matter of energy too). But let's skip those complications for now.

A surprisingly large number of students have instead counted like this:
- My TV uses 100 W
- I will watch it for 8 hours - that's 800 Wh
- An energy slave generates 100 W
- 800/100 = 8 and I thus need 8 slaves to run my TV.

Some of you have even written 800 Wh (or 0.8 kWh) on one line and then on the next line changed the unit by unproblematically transforming those 800 Wh into 800 W so as to better align it with the measure of how much energy a slave can generate - despite the fact that these are two totally different units of measure.

The result is a "category mistake". It is equivalent to saying that if I drive my car at the speed of 100 km/h for 8 hours, the resulting speed will be 800 km/h. That's naturally not the case. The distance you will have driven after 8 hours is 800 km but and that's of course very different from the previous erraneous statement about "the resulting speed".