Why does the vacuum reduce convection and conduction but not radiation (in aDewar flask)?
part b:
A small object of mass m at 100 C is placed into an equal mass of water at 0 C in a calorimeter. The
specific heat capacity of the object is half that of the water. Assuming there are no energy transfers to the
environment or to the calorimeter, the final equilibrium temperature of the object plus water will be what?
the answer in the book says 33 C but how???
1st part: Convection and conduction require matter whereas radiation does not.
Convection is the movement of a fluid (gas or liquid) due to differences in temperature – i.e., no fluid, no convection.
Conduction is the transfer of the kinetic energy of particles through collisions. I.e., no particles, no collisions, no transfer.
I’ll come back to the 2nd part in a sec…
__________________
You need to use the equation for specific heat capacity
Q = MC∆T
Q = thermal energy, M = mass, C = specific heat capacity, ∆T = change in temp (final temp – initial temp)
As the energy lost by the object equals the energy gained by the water, the overall energy equals zero:
Q water + Q object = 0
Therefore:
MC∆T (water) + MC∆T (object) = 0
From now on I’ll use the lowercase “w” and “o” to indicate water and object. I’ll also swap in (Te – Tw) and (Te – To) for the ∆T. Te = the equilibrium temp, Tw = the initial temp of the water, To = the initial temp of the object
Rearrange the above equation using my new symbols:
MwCw(Te – Tw) = – MoCo(Te – To)
Okay, now to cancel some stuff.
Mw = Mo, so they cancel
Cw(Te – Tw) = – Co(Te – To)
As “The specific heat capacity of the object is half that of the water” Cw = 2Co, so sub this in
2Co(Te – Tw) = – Co(Te – To)
Then cancel the Co
2(Te – Tw) = -(Te – To)
Now expand the brackets (don’t forget the negative on the RHS)
2Te – 2Tw = -Te + To
Rearrange in terms of Te:
3Te = 2Tw + To
Now we can sub in the numbers (Tw = 0, To = 100°C)
3Te = 2*0 + 100
Te = 100/3 = 33.3°C
Hope that helps. Write it out yourself to try and really understand it.
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