Solve Newton's Cooling Law: Find m with c and t=10 mins

In summary, the problem involves finding the constant temperature of the medium (m) given an object's initial temperature (60oF) and subsequent temperature readings (45oF and 36oF) at specific time intervals (5 mins each). This can be solved using Newton's Law of Cooling, which involves finding the constant k and using it to calculate m.
  • #1
Nope
100
0

Homework Statement


An object of temperature 60oF is placed in a medium maintained at a constant temperature moF. At the end of 5 mins thetemperature of the object is 45 oF and after another 5 mins its temperature is 36 oF.
Find m


Homework Equations



y=cekt+m

The Attempt at a Solution


when t=0,c+m=60
how would you find c and m??
thx
 
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  • #2
Nope said:

Homework Statement


An object of temperature 60oF is placed in a medium maintained at a constant temperature moF. At the end of 5 mins thetemperature of the object is 45 oF and after another 5 mins its temperature is 36 oF.
Find m


Homework Equations



y=cekt+m

The Attempt at a Solution


when t=0,c+m=60
how would you find c and m??
thx
Perhaps you should try solving directly from the formula for Newton's Law of Cooling.

i.e. dT/dt = -k(T - Tambient)
where T = temp, t = time, k is a positive constant.
 

Related to Solve Newton's Cooling Law: Find m with c and t=10 mins

1. How do you use Newton's Cooling Law to solve for m with given values of c and t?

To solve for m using Newton's Cooling Law, we can use the formula: m = c * t. Simply plug in the given values of c and t, and solve for m.

2. Can Newton's Cooling Law be used for any cooling system?

No, Newton's Cooling Law is specifically used for systems where the temperature change is caused by convection, which is the transfer of heat by the movement of a fluid. It may not be applicable for other types of cooling systems.

3. What is the unit for m in Newton's Cooling Law?

The unit for m in Newton's Cooling Law is usually in joules per second per degree Celsius (J/s/°C) or watts per degree Celsius (W/°C). This represents the rate at which the system is losing heat.

4. Can Newton's Cooling Law be used for systems with varying temperatures?

Yes, Newton's Cooling Law can be used for systems with varying temperatures as long as the temperature change is caused by convection and the initial and final temperatures are known.

5. How accurate is Newton's Cooling Law in predicting temperature changes?

The accuracy of Newton's Cooling Law depends on various factors such as the specific heat capacity of the material, the surface area, and the rate of convection. It is a simplified model and may not account for all variables, so the accuracy may vary in different situations.

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