Question by the last: What is the temp of the thermometer at 1 min? How long to reach 15 degree F?
A thermometer is removed from a room where the temperature is 70 degrees F and is taken outside, where the air temperature is 10 degrees F. After one-half minute the thermometer reads 55 degrees F.

What is the reading of the thermometer at t = 1 min?

How long will it take for the thermometer to reach 15 degrees F?

Best answer:

Answer by Scruff
Use Newton’s Law of Cooling:

T = T(environment) + (T(initial) – T(environment)) * e^(-r * t)

where
T = current temp
T(environment) = 10
T(initial) = 70
r = rate of cooling
t = time

You know that after t = .5 min, T = 55. Plug these values in and solve for r:

55 = 10 + (70 – 10) * e^(-.5r)
45 = (60) * e^(-.5r)
.75 = e^(-.5r) <- take the natural log of both sides
-.288 = -.5r
>>> r = .575

Now that you know r, solve for T at t=1min:

T = 10 + (70 – 10) * e^(-.575*1)
T = 10 + 60 * .563
>>> T = 43.8 degrees

Likewise solve for t when T=15

15 = 10 + (70 – 10) * e^(-.575t)
5 = 60e^(-.575t)
.0833 = e^(-.575t) <- take the natural log of both sides
-2.49 = -.575t
>>> t = 4.32 min

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Question by Saleha Ali: You put a thermometer in a pot of hot water and record thee reading. What temperature?
You put a thermometer in a pot of hot water and record thee reading. What temperature
have you recorded?
I. The temperature of the water;
II. The temperature of the thermometer;
III. An equal average of the temperature of the water and thermometer;
IV. A weighted average of the water and thermometer, with more emphasis on the
temperature of the water.
V. A weighted average of the water and thermometer, with more emphasis on the
temperature of the thermometer.
Explain your above selected answer as well.

Best answer:

Answer by dogsafire
IV. A weighted average of the water and thermometer, with more emphasis on the
temperature of the water.

Before you place the thermometer in the hot water it is at room temperature. Despite the fact that thermometer manufacturers try to keep the mass of thermometers small so that they can react quickly, a thermometer still has sufficient mass that it must be heated to the temperature of its surroundings before it can provide an accurate temperature. During that time period, you will some combination of the temperature of the thermometer and the temperature of the water. But because there is much more mass in the water than the thermometer, the reading will be weighted toward the water’s temperature (unless you take a reading very, very quickly after putting the thermometer into the water, in which case, the thermometer’s temperature will matter more than the water’s temperature)

Add your own answer in the comments!

Macho man

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Question by dabestanswerer…: Thermometer?
For my science fair project, I need to measure the temperature of the air inside a basketball. But the problem is that I don’t know of a thermometer that is so small that I can fit it inside a basketball.

Thanks

Best answer:

Answer by -Matt-
Pierce a hole in the basketball and stick the thermometer in it?
Or find a container you could trap the air in if you let it out of the basketball.

Know better? Leave your own answer in the comments!