Answers to Problems on (Laws of Thermodynamics) HC Verma's Questions for Short Answer (1-8)

 Q#1

Should the internal energy of a system necessarily increase if heat is added to it?  

Answer:
The increase in the internal energy (ΔU) of a system is equal to the amount of heat given (ΔQ) minus the amount of work (ΔW) done by it.

ΔU = ΔQ - ΔW

If ΔW = ΔQ, the change in internal energy is zero. So the internal energy does not necessarily increase if heat is given to the system.  

Q#2
Should the internal energy of a system necessarily increase if its temperature is increased?  

Answer:
The internal energy of a system increases if the total kinetic energy of all the molecules increases and this thing increases with the increase in the temperature. Hence the internal energy of a system necessarily increases if its temperature is increased.  

 Q#3
A cylinder containing gas is lifted from the first floor to the second floor. What is the amount of work done on the gas? What is the work done by the gas? Is the internal energy of the gas increased? Is the temperature of the gas increased?  

Answer:
Since there is no change in the volume of the gas, no work is done on the gas nor any work is done by the gas.
No, the internal energy of the gas is not increased because the systematic movement of a gas sample has no effect on temperature.

Q#4
A force is applied on a block of mass M. The block is displaced through a distance d in the direction of the force. What is the work done by the force on the block? Does the internal energy change because of this work?  

Answer:
The work done by the force F here = Fd.

No, the internal energy of the block does not change. This work done is reflected either as a change of kinetic energy or potential energy.

Q#5
The outer surface of a  cylinder containing gas is rubbed vigorously by a polishing machine. The cylinder and its gas become warm. Is the energy transferred to the gas heat or work?  

Answer:
Since the volume of the gas does not change, the energy transferred is not due to work. The energy to the gas is transferred by the cylinder which is in the form of heat that is generated due to friction.    

Q#6
When we rub our hands they become warm. Have we applied heat to the hands?  

Answer:
No. It is the mechanical work done by us to overcome the force of friction between the hands which converts into heat energy.  

 Q#7
A closed bottle contains some liquid. The bottle is shaken vigorously for 5 minutes. It is found that the temperature of the liquid is increased. Is heat transferred to the liquid? Is work done on the liquid? Neglect expansion on heating.  

Answer:
No, heat is not transferred to the liquid.
Work done is equal to the force times displacement. Assuming that the bottle is kept at the initial position after shaking, the displacement is zero. So no work is done on the liquid. But in the shaking of the liquid work is done against the viscous forces, also it increases the total kinetic energy of the molecules. So the internal energy of the liquid and temperature increases.    

Q#8
The final volume of the system is equal to the initial volume in a certain process. Is the work done by the system necessarily zero? Is it necessarily nonzero?  

Answer:
If the final volume of the system is equal to the initial volume, then the process is either isochoric or cyclic. The cyclic process may be either reversible or irreversible. In the isochoric process, the work done is zero. In the reversible process, the done by the system and the work done on the system is compensated and final work done is zero. In the irreversible process, the work done by the system is not equal to the work done on the system. Hence the final work done is not zero.
Thus the answer to both the questions is "no".  

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