VDU_Physics_2_012  
 

 

Solved University-Physics Problems

Physics 2.-  Specific Heat

Javier Montenegro Joo

jmj@VirtualDynamicsSoft.com

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[1] Determine how much heat is required to raise the temperature of a 25 kg aluminum cylinder, which contains 20 Lt of water, from 24 oC to 110 oC

Solution.-

Heat separately the aluminum cylinder and the water and then sum both quantities.

 

 

     
 

[2] Determine the equilibrium temperature when 300 cm3 of water at 80 oC are poured into a 100 gr glass bottle which is at 22 o

Solution.-

Since the water is hotter than the glass, the former losses heat and this is taken by the latter:

 
     
 

[3] 400 cm3 of alcohol at 80 oC are poured into a 125 gr cooper vessel which is at 24 oC. Calculate the equilibrium temperature. It is known that 4.5 gr of alcohol occupy 5 cm3.

Solution.-

Since the alcohol is hotter than the vessel, heat from the former is transferred to the latter.

Density and mass of alcohol:

 
     
 

[4] Determine the final temperature of a 800 gr copper ball at 22 C when it is exposed to a flamethrower which supplies 8000 J of heat.

Solution .-

 
 

 

 
 

[5] Two 400 gr balls are at 24 C -one of copper and the other of aluminum- are simultaneous heated with a flamethrower which supplies 3510 J of heat to each ball. Determine the final difference of temperatures between the balls.

Solution .-

 
     
 

[6] A 800 gr brick of copper at 117.75 F is placed into a freezer that absorbs 8000 J of heat from the brick. Find the final temperature of the brick.

Solution

In this case heat is being extracted from the sample and hence the final temperature is lower than the initial one, then the equation must be

 
     
 

[7] A 0.5 kg aluminum ball freely falls from 600 m height on a 1 kg copper block. Assuming that all the energy from the ball is transferred to the block, find the increment in the temperature of the block. If the initial temperature of the copper block was 24 C, what would be its final temperature?

Solution

In this case the gravitational potential energy of the falling ball is converted into kinetic energy of the ball and, at the impact on the block this energy becomes heat, thus heating up the block and increasing its temperature, then the available heat is Q = Ep = mgh

 
     
 

[8] A 10 gr lead (Pb) projectile is fired horizontally with a velocity of 300 m/s and impacts on a sandbag. Assuming that there is no energy transfer from the projectile to the sand, determine the increase in the temperature of the projectile.

Solution

The velocity of the projectile implies that it has kinetic energy. At the impact the projectile stops and, since there is no energy transfer, all the available energy heats up the projectile, thus increasing its temperature.

 
     
 

[9] A 50 kg metal bar is heated to 100 C and then introduced into a vessel containing 10 kg of water at 20 C.  Determine the specific heat of the metal if the equilibrium temperature of water and metal is 26 C.

Solution         

Since the metal bar is hotter than the water, the metal piece cools down and the water heats up, in other words, the metal piece loses heat and this heat is absorbed by the water.  Notice in this problem that the change in temperature of the vessel is not being taken into account, actually part of the metal heat is shared by the vessel and by the water.

 
     
 

[10]  A  50 kg metal bar is heated to 100 C and then introduced into a vessel containing 10 kg of water at 20 C.  Determine the equilibrium temperature of water and metal if it is known that the specific heat of the metal is  67.88 J/kg C

Solution  

Since the metal bar is hotter than the water, the metal piece cools down and the water heats up, in other words, the metal piece loses heat and that heat is absorbed by the water.

 
     
 

[11]  A 4 kg aluminum block that is at 423.08 C is introduced in an 8 kg iron container containing 30 lt of water at 15 C.  Determine the equilibrium temperature of water.

Solution.-

In this case the aluminum block is hotter than the water and the iron vessel. Then there will be a heat transfer from the block to the vessel and water. The heat lost by the aluminum is absorbed by the water and the iron:

 
     
 

[12] A 4 kg aluminum block is introduced in an 8 kg iron vessel containing 30 lt of water at 15 C.   After sometime the equilibrium temperature of the water is  26.29 C.   Determine the initial temperature of the aluminum block.

Solution.-

Since the equilibrium temperature is higher than that of the water and iron it means that the initial temperature of the aluminum block was the highest of the three and, the heat lost by the aluminum was absorbed by the iron and water.

 
     
     
 

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