Saturday, December 4, 2010

Thermodynamics test - q6

I have a question on the physics thermo quiz - Q 6.  In the solution they sub the info into the equation and then add in (1m/100cm) - it is because there is a cube - I had converted the cm cubed into .1 cubed which left me numerically with the right number but the wrong exponent....
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To go over this question, I'll first copy it down:
A balloon holds 100 cubic centimeters of air. If the temperature of the air is raised from 300 K to 350 K, what is the change in the volume of the balloon? (βair = 3.67 x 10-3 °C-1).
This uses our equation for volume expansion:  ΔV = βVΔT.  If we start plugging in, we get:

ΔV = 3.67 x 10-3 C°-1(100 cm3)(50°C)

Note that a change in Kelvins is equal to that change in Celsius.  So, we have a little problem, as you mention – 100 cm3 is given, but they want m3 in the answer.  To convert here, we have to use the conversion factor that 1 m = 100 cm.  However, since we have cubic units on both sides, we’ll have to use that (1 m)3 = (100 cm)3, or 1 m3 = 1000000 cm3 (that’s 106).  Thus, we can say

ΔV = 3.67 x 10-3 C°-1(100 cm3)[1 m/ 106 cm3](50°C)

or

ΔV = 3.67 x 10-3 C°-1[10 -4 m3](50°C) = (3.67 x 10-7)(50) = between 150-200 x 10-7 = between 1.50-2.00 x 10-5

The big takeaway then is that we have to cube the conversion factor to make it work for volume here!

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