Bukhovtsev-et-al-Problems-in-Elementary-Physics

HEAT. MOLECULAR PHYSICS 271
301. On the basis of the law of conservation of energy,
mgl =mv 2 + k (1-/0 ) 2 + Q
2 2
where l is the length of the cord at the moment when the washer leaves it.
• On the other hand, we can write that
mv 2
mgl=T+W l + W 2
where WI = flo is the work of the force of friction acting, on the washer (the
washer travels a path of lo relative to the cord), and W s=f (1-1 0
) is the work
of the force of friction acting on the cord. Therefore,
Using Hooke's Law
we find that
k (1-1 0 )2
Q=W 1+W2 2
f=k (l-Io>
f2
Q=flo+ 2k
The work W1 is used entirel y to liberate heat. Only half of the work W2 = ~ ,
however, is converted into heat, the other half producing the potential energy
k (/-1 0 )2
2 .
302. The electric current performs the work W =PT. At the expense of
this work the refrigerator will lose the beat QI=qH+ qct ; where c is the
heat capacity of water and H is the heat of fusion of ice. According to the
law of conservation of energy, the amount of heat liberated in the room will be
Q. = W+Q2=Pt:+qct+qH
since in the final run the energy of the electric current is converted into heat.
303. The temperature in the room will rise. The quantity of heat liberated
in a unit of time will be equal to' the power consumed by the refrigerator,
since in the final run the energy of the electric current is converted into heat,
and the heat removed from the refrigerator is returned again into the room.
304. It is more advantageous to use a refrigerator that removes heat from
the outside air .and liberates it in the room. The heat liberated in the room
in a unit of time is P+Q2' where P is the power consumed by the refrigerator
and Q, is the heat removed from the outside air in a unit of time (see
Problem 302).
It is only the high cost and complicated equipment that prevent the use
of such thermal pumps for heating at present.
305. When salt is dissolved, its crystal lattice is destroyed. The process
requires a certain amount of energy that can be obtained from the solvent.
In the second case, part of the intermolecular bonds of the crystal lattice
have already been destroyed in crushing the crystal. For this reason, less
energy is required to dissolve the powder and the water will be higher in
temperature in the second vessel. The effect, however, will be extremely
negligible.