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مسائل وتمارين
Problems
Heat capacity
and specific heat
(1)
Consider Joule's apparatus described in lecture 3. The two masses are
1.5kg each and the tank is filled with 200g of water. What is the increase
in the temperature of the water after the masses fall through a
distance of 3m? ANS.
0.105oC
(2) How
many calories of heat are required to raise the temperature of 3kg of
aluminium from 20oC to 50oC?
(3)
Copper pellet, each of mass 1g are heated to 100oC. How many
pellets must be added to 500g of water initially at 20oC to
make the final equilibrium temperature 25oC?
(4) If
200g of water is contained in a 300g aluminium vessel at 10oC
and an additional 100g of water at 100oC is poured into the
container, what is the final equilibrium temperature of the system?
ANS. 34.7oC
(5) How
much heat must be added to 20g of aluminium at 20oC to melt it
completely? ANS.13.3kJ
(6) A 20g ice cube at
0oC is heated until 15g has become water at 100oC
and 5g has been converted to steam. How much heat was added to do this?
ANS.
26.3kJ
(7)
Determine the final state when 20g of 0oC ice and 10g of 100oC
steam are mixed together in an insulated container.
ANS. 26.7g liquid and 3.35g vapor at 100oC
(8) A
3g bullet traveling with a speed of 400m/s stopped by large tree. If
all of its kinetic energy is converted to thermal energy in the bullet,
find increase in the temperature of the bullet.
ANS.434oC this heat will rapidly
converted to the tree
Work and Heat
 (9)
A gas expands from I to F
along three possible paths as indicated by the
figure. Calculate the work done by the gas along the
paths IAF, IF, IBF.
ANS. 810J, 506J ,203J
(10) An
ideal gas is enclosed in a cylinder. There is a movable piston on top of
the cylinder. The piston has a mass 0f 8000g and an area of 5cm2
and is free to slide up and down, keeping the pressure of the gas
constant. How much work is done as temperature of 0.2moles of the
gas is raised from 20oC to 300oC?
ANS. 466J
The first law of thermodynamics
(11) As
the gas expand from I to F as shown in the figure of problem (9).
The heat added to the gas is 400J when the gas goes from I to F along the
diagonal path. (a) What is the change in internal energy of the gas? (b)
How much heat must be added to the gas for the indirect path IAF to give
the same change in internal energy?
(12) A
gas is compressed at constant pressure of 0.8atm from a volume of 9L to a
volume of 2L. In the process 400J of heat energy flows out of the gas. (a)
What is the work done by the gas ? (b) What is the change in internal
energy of the gas? ANS. (a) -567J , (b) 167J
 (13)
One mole gas initially at
pressure of 2atm and of 0.3L has an internal energy equal to 91J. In its
its final state, the pressure is 1.5atm, the volume is 0.8L, and the
internal energy equals 182J. For the three paths IAF, IBF and IF,
calculate (a) the work done by the gas and (b) the net heat transferred in
the process. If Ui=91J and Uf=182J.
ANS. (a) 76J, 101J ,88.6J ANS. (b) 167J, 192J,
180J
 (14)
A gas is taken through the cyclic process described in the figure. (a)
Find the net heat transferred to the system during one complete cycle. (b)
If the cycle is reversed, that the process goes along ACBA, what is the
net heat transferred per cycle? ANS. (a) 12kJ,
(b) -12kJ
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