Heat Temperature and Thermal Expansion Exam1 and  Problem Solutions

1. Two thermometer X shows boiling point of water 220X and freezing point of water 20X and Y shows boiling point of water 120 Y and freezing point of water -40Y. If thermometer X shows 100X, find the value that thermometer Y shows.

thermometer_1

 

 

 

 

 

 

 

(X-20)/200=(Y-(-40))/160

(X-20)/20=(Y+40)/16

Y=240Y

 

2. Two matters have specific heat capacities c and 2c. If we give Q and 4Q heat to these matters, changes in the temperatures of them become equal. If the matter A has mass m, find the mass of matter B in terms of m.

Heat gained, lost by the matters is found with following formula;

Q=m.c.ΔT

Heat gained by A and B;

Q=mA.c.ΔT

4Q=mB.2c.ΔT

mB=2mA

mB=2m

 

3. A and B matters have equal masses. Find the ratio of cA/cB.

heat_1

 

 

 

 

 

 

 

 

 

Q=m.c.ΔT

30=m.cA.(10-0)

30=m.cB(20-0)

cA/cB=2

 

4.

heat_2

 

 

 

 

 

 

 

 

Table given above shows initial lengths, changes in temperatures and changes in the length of 3 rods. Find whether these rods are made of same matters or not.

ΔL=L0.α.ΔT

αA=ΔL/2L.ΔT

αB=3.ΔL/3L.2ΔT

αC=ΔL/4L.ΔT

αABC

Thus, A and B can be same matter but C is different from them.

5. Three cylinders made of same matter and at same temperature, are placed on a platform. Same amount of heat given to the cylinders make same amount of change in their temperature. Find the relation between changes in the lengths of these cylinders.

 

 heat_3

 

 

 

 

 

 

 

If we say volume of X is V, then volume of Y is also V and Z is V/2. There is a linear relation between volumes and mass, we use this relation in solution of the problem.

Q=m.c.ΔTX, ΔTX=T

Q=m.c.ΔTY, ΔTY=T

Q=m/2.c.ΔTZ, ΔTZ=2T

Changes in the lengths of cylinders;

ΔLX=h.α.T=ΔL

ΔLY=2h.α.T=2ΔL

ΔLZ=h.α.2T=2ΔL

ΔLY=ΔLZ>ΔLX

 

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