How Does Newton's Law of Cooling Affect Heat Loss Calculations?

In summary: What is the specific heat capacity of the metal given the data provided?In summary, a 1kg metal ball is heated by a 20W heater in a room at 20°C until it reaches a steady temperature of 50°C. The rate of heat loss to the surroundings at 50°C is equal to the heat gained by the ball. Using Newton's law of cooling, the rate of heat loss to the surroundings at 30°C is 20/3 watts. Assuming the temperature of the ball rises uniformly from 20°C to 30°C in 5 minutes, the total heat loss to the surroundings during this period can be calculated. The specific heat capacity of the metal can also be determined using the given data.
  • #1
Radical
1
0

Homework Statement


A metal ball of mass 1kg is heated by means of a 20W heater in a room at 20°C. The temperature of the ball becomes steady at 50°C. (a) Find the rate of loss of heat to the surrounding when the ball is at 50°C. fa) Assuming Newton's law of cooling, calculate the rate of loss of heat to the surrounding when the ball is at 30°C. (c) Assume that the temperature of the ball rises uniformly from 20°C to 30°C in 5minutes. Find the total loss of heat to the surrounding during this period, (d) Calculate the specific heat capacity of the metal.

Homework Equations


dT/dt= -k(T-Ts) where Ts is temperature of surrounding and T is temperature of the body.
Stefan's law ∆U= sigma e AT^4

The Attempt at a Solution


For 1st part as the ball is in steady state at 50 °C hence amount of heat gained by ball = heat lost to the surroundings by radiation. Hence it is equal to 20 watt.

2nd part's the answer given is 20/3 watt but the answer I am getting is nowhere close.
I used the Stefan's law to find the answer.
 
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  • #2
Stefan's law has nothing to do with Newton's law of cooling. Newton's law of cooling describes heat conducted to the surroundings, not radiated. You need to use Newton's law of cooling.
 
  • #3
Radical said:

Homework Statement


A metal ball of mass 1kg is heated by means of a 20W heater in a room at 20°C. The temperature of the ball becomes steady at 50°C. (a) Find the rate of loss of heat to the surrounding when the ball is at 50°C. fa) Assuming Newton's law of cooling, calculate the rate of loss of heat to the surrounding when the ball is at 30°C. (c) Assume that the temperature of the ball rises uniformly from 20°C to 30°C in 5minutes. Find the total loss of heat to the surrounding during this period, (d) Calculate the specific heat capacity of the metal.

Homework Equations


dT/dt= -k(T-Ts) where Ts is temperature of surrounding and T is temperature of the body.
Stefan's law ∆U= sigma e AT^4

The Attempt at a Solution


For 1st part as the ball is in steady state at 50 °C hence amount of heat gained by ball = heat lost to the surroundings by radiation. Hence it is equal to 20 watt.

2nd part's the answer given is 20/3 watt but the answer I am getting is nowhere close.
I used the Stefan's law to find the answer.
Who says that the rate of heat loss is dominated by radiative heat transfer? What does Newton's law of cooling tell you about part 2?
 

Related to How Does Newton's Law of Cooling Affect Heat Loss Calculations?

1. What is Newton's law of cooling?

Newton's law of cooling is a scientific principle that explains the rate at which an object cools down when placed in a different temperature environment. It states that the rate of temperature change of an object is directly proportional to the difference between its initial temperature and the temperature of the surrounding environment.

2. Who is Sir Isaac Newton and how is he related to this law?

Sir Isaac Newton was a famous English physicist and mathematician who is credited with discovering the law of cooling. He observed that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, and this relationship is known as Newton's law of cooling.

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

Yes, Newton's law of cooling can be applied to all objects, as long as they are not undergoing any chemical reactions or phase changes. It is especially useful for predicting the cooling rate of liquids and gases.

4. How can Newton's law of cooling be expressed mathematically?

The mathematical expression for Newton's law of cooling is:
dT/dt = -k(T - Ts)
Where dT/dt is the rate of temperature change, k is the cooling constant, T is the temperature of the object, and Ts is the temperature of the surrounding environment.

5. Are there any real-life applications of Newton's law of cooling?

Yes, Newton's law of cooling has many practical applications, such as in the design of refrigerators and air conditioning systems, determining the time of death in forensic science, and predicting the temperature of food in cooking and food preservation processes.

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