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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).
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 m3 / 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!
The big takeaway then is that we have to cube the conversion factor to make it work for volume here!
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