What was the temperature of the object?

In summary, the temperature of an object initially placed in a room at 20 degrees Celsius can be found by using Newton's law of cooling and solving for To, the initial temperature. This can be done by subtracting T(4) and T(8) values and solving for To.
  • #1
Math10
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Homework Statement


An object is placed in a room where the temperature is 20 degrees Celsius. The temperature of the object drops by 5 degrees Celsius in 4 minutes and by 7 degrees Celsius in 8 minutes. What was the temperature of the object when it was initially placed in the room?

Homework Equations


Newton's law of cooling: T(t)=Ta+(To-Ta)e^(-kt)

The Attempt at a Solution


T(t)=Ta+(To-Ta)e^(-kt)
I know that I need to solve for To, which is the initial temperature but I don't know what to do.
 
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  • #2
Rewrite Newton in terms of delta T and see if that gives you any ideas.
 
  • #4
Math10 said:

Homework Statement


An object is placed in a room where the temperature is 20 degrees Celsius. The temperature of the object drops by 5 degrees Celsius in 4 minutes and by 7 degrees Celsius in 8 minutes. What was the temperature of the object when it was initially placed in the room?

Homework Equations


Newton's law of cooling: T(t)=Ta+(To-Ta)e^(-kt)

The Attempt at a Solution


T(t)=Ta+(To-Ta)e^(-kt)
I know that I need to solve for To, which is the initial temperature but I don't know what to do.
When t= 4 min, T(4)= Ta+ (To- Ta)e^(-4k)= 15. When t= 8 min, T(8)= Ta+ (To- Ta)e^(-8k)= 13.
What do you get if you subtract e^(-8k)T(4)- e^(-4k)T(8)?

You are asked to find T(0)= To.
 
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  • #5
I got it! Thanks everyone for the help!
 

What was the temperature of the object?

The temperature of an object refers to the average kinetic energy of its molecules. It can be measured using a thermometer and is typically expressed in degrees Celsius (°C) or Fahrenheit (°F).

How is temperature different from heat?

Temperature and heat are related but different concepts. Temperature measures the average kinetic energy of molecules in an object, while heat is the total energy transferred between two objects due to a temperature difference.

What factors can affect the temperature of an object?

The temperature of an object can be influenced by factors such as the amount of heat it receives or loses, its size, its material, and its surroundings. Changes in temperature can also be caused by physical or chemical processes occurring within the object.

How can temperature be converted between different units?

The most commonly used temperature scales are Celsius, Fahrenheit, and Kelvin. To convert between these units, you can use the following formulas: - Celsius to Fahrenheit: F = (C x 9/5) + 32 - Fahrenheit to Celsius: C = (F - 32) x 5/9 - Celsius to Kelvin: K = C + 273.15 - Kelvin to Celsius: C = K - 273.15

Can the temperature of an object ever reach absolute zero?

Absolute zero is the lowest possible temperature, equivalent to 0 kelvins. At this temperature, all molecular motion stops. While it is theoretically possible to reach absolute zero, it is impossible to achieve in practice. The lowest recorded temperature in a laboratory is 100 picoKelvins above absolute zero.

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