Radiation and heat transfer stuff

[ilovephysics]

1) A blackended, solid copper sphere of radius 4.0cm hangs in a vacuum in a enclosure whose walls have a temperature of 20.0 celcius. If the sphere is initially at 0 celcius find the rate at which the temp. changes assuming that heat is transferred by radiation only

2 questions:
- do we assume emissivity is unity? (1)
- how do you find the rate the temp changes after you find the rate of energy radiation (work which is joules/second )

2)A crate of fruit with mass 35.0kg and specific heat capacity 3650 J/kg K slides down a ramp inclined at 36.8 degrees below the horizontal. The ramp is 8.00m long. a) if the crate was at rest at the top of the incline and has a speed of 2.50m/s at the bottom, how much work was done on the crate by friction? b) if an amount of heat equal to the magnitude of the work done by friction goes into the crate of fruit and the fruit reaches a uniform final temperature, what is its temperature change?

-i think this is a simple question about friction and stuff but i don't remember how to calculate that stuff, and we are not given the coefficient of kinetic/static friction so I am kinda stuck
-as for part b), I am not sure which equation to use to get the change in temp.

 

[siddharth]

1)
For the first sum, I think you need the Heat capcity of the copper sphere to solve the question. Now dq=ms dT, dq/dt = ms(dT/dt) where T is temperature and t is time.
Use this and stefan's law, and you should get your answer. As the sphere is blackended, we should assume the emissivity is 1, though this is not strictly true.

 

[ilovephysics]

thanks, but how do i know what the mass of the sphere is?

 

[siddharth]

If you know the density of copper, and calculate the volume of the copper sphere, from that you can find the mass.