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

[Radical]

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.

 

[Orodruin]

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.

 

[Chestermiller]

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?