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Cheetah3D tutorial 3: Modeling a Cup/Mug

Cup Mug

A cup of coffee at 196 degrees is poured into a mug and left in a room at 73 degrees.?

A cup of coffee at 196 degrees is poured into a mug and left in a room at 73 degrees. After 7 minutes, the coffee is 147 degrees. Assume that the differential equation describing Newton's Law of Cooling is (in this case) dT/dt= k(T-73)

This is a separable differential equation:

dT/dt = k*(T - 73)

dT/(T-73) = kdt

ln(T-73) - ln(c) = k*t

where ln(c) is the constant of integration.

ln((T-73)/c) = k*t

The cup is initially (at t = 0) at 196 deg, so

ln((196-73)/c) = 0

(196-73) = c = 123

Now go back and solve for k. When t = 7min, T = 147 deg, so:

ln((147-73)/123) = k*7min

k = [ln(74/123)]/7min

k = -0.0726/min

So:

T(t) = 73 + c*exp(k*t) = 73 + 123*exp(-0.0726*t/min)

The temperature at t = 17min is:

T(17min) = 73 + 123*exp(-0.0726*17) = 108.8 deg

Going back to the logarithmic form of the solution:

ln((T-73)/123)*min/(-0.0726) = t

The coffee is 100 deg when:

ln((100-73)/123)*min/(-0.0726) = t

t = 20.9 min

Cup or Mug

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Tags: coffee, coffee cup mug, cup mug, cup mug company, cup mug difference, cup mug holder, design, mug, shopping, tea

This entry was posted on Saturday, December 8th, 2001 at 3:24 am and is filed under China. You can follow any responses to this entry through the RSS 2.0 feed. Responses are currently closed, but you can trackback from your own site.