When was the thermometer brought indoors?

In summary, the thermometer was brought indoors at time t=0 and the temperature was T0=60 degrees Fahrenheit. The time it took for the thermometer to cool from 80 F to T0 when the background temperature was 20 F can be calculated using the formula (80-T0)/60=e^(-k*t0). Similarly, the time it took for the thermometer to warm up from T0 to 71 F when the background temperature was 80 F can be calculated using the formula (71-T0)/60=e^(k*t1). By setting up a third equation, t0+t1=10, we can solve for all three unknowns and determine the exact time and temperature when the thermometer was brought indoors.
  • #1
BeefBowl
8
0

Homework Statement


at t=0; thermometer reading (x) =80 F (taken outside where the air temp is 20 F)
at t=3; x=42 F
then the thermometer is brought inside where the air is at 80 F.
at t=10; x=71 F
When was the thermometer brought indoors?

Homework Equations


temp=ambient temperature; x= present temp of the body
x - temp=Ce-kt

The Attempt at a Solution



first I get the value of k: t=0; x=80
x=Ce-kt +20
C=60

x=60e-kt +20; t=3;x=42
k=0.334

Now, when brought inside:
at t=0, x=??
x-80=Ce-0.334t
C=x-80

And I am currently stuck up in here. If answered, could someone explain how does it happen? Thanks in advance!
 
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  • #2
Call the temperature when it's brought in T0, and call the time it's brought in t0. Then t0 is the time to cool from 80F to T0 when the background is 20F, right? That means (80-T0)/60=e^(-k*t0), also right? Now call t1 the time to warm up from T0 to 71F when the background is 80F. Can you write a similar formula for t1? If you can do that then you've got two equations in the three unknowns t0, T0 and t1 (since you already know k). Now you need one more equation. How about t0+t1=10?
 
  • #3
Thanks Dick! I get it now.
 

1. What is Newton's law of cooling?

Newton's law of cooling is a mathematical equation that describes the rate at which an object cools in a surrounding environment. It states that the rate of heat loss of an object is directly proportional to the temperature difference between the object and its surroundings.

2. How does Newton's law of cooling work?

According to Newton's law of cooling, the rate of heat loss is determined by the difference in temperatures between the object and its surroundings. As the object's temperature decreases, the rate of heat loss also decreases, eventually reaching a state of thermal equilibrium where the object and its surroundings have the same temperature.

3. What are the factors that affect Newton's law of cooling?

The factors that affect Newton's law of cooling include the initial temperature of the object, the temperature of its surroundings, and the thermal conductivity of the object. Other factors such as air flow and humidity can also have an impact on the rate of heat loss.

4. How is Newton's law of cooling used in real life?

Newton's law of cooling is used in various real-life applications, such as in refrigerators, air conditioning systems, and cooking. It is also used in weather forecasting to predict changes in temperature over time.

5. Can Newton's law of cooling be applied to all objects?

Newton's law of cooling can be applied to most objects, as long as they are in contact with a surrounding environment and have a measurable temperature. However, the law may not be accurate for objects that undergo significant changes in temperature, such as phase changes from solid to liquid.

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