AP Physics B – Free Response Questions (for Practice) on Thermodynamics

I give below two typical free response practice questions on thermodynamics:

(1) One mole of an ideal mono atomic gas at standard temperature (T₀) and standard pressure (P₀) is contained in a cylinder fitted with a frictionless piston. The gas has volume V₀ under these conditions. The following three operations are performed on the gas:

(i) The gas is heated at constant volume so that its pressure is doubled.

(ii) The gas is then made to undergo isothermal expansion so that the pressure is restored to the initial value.

(iii) The gas then undergoes an isobaric compression so that its volume is restored to the initial value.

Now, answer the following questions:

(a) Draw a P-V diagram to represent the processes numbered (i), (ii) and (iii) above, marking the initial (as well as final) state of the gas by point A, and the intermediate states by points B and C.

(b) What is the final temperature of the gas? Justify your answer.

(c) During the process (i) what is the work done by the gas? Justify your answer.

(d) Calculate the volume (V₂) of the gas at the end of the isothermal expansion mentioned in process (ii).

(e) If the work done by the gas during its isothermal expansion is given to be 1.45P₀V₀, calculate the net work done during the entire cycle of operations involving the processes (i), (ii) and (iii).

(2) Two moles of nitrogen are contained in a vertical conducting cylinder provided with a frictionless piston of negligible mass and area equal to 1.5×10^–2 m² (Fig.). Nitrogen behaves as an ideal gas. It is brought to the following states through a sequence of operations as follows:

(i) Initially the temperature of nitrogen is the same as the laboratory temperature of 27º C and its volume is V₁. This state of the gas is designated as state A

(ii) The piston is now pulled up with a gradually increasing force of final value 60 N, maintaining the temperature at 27º C itself. The volume of the gas now becomes V₂. This state of the gas is designated as state B.

(iii) The temperature of the gas is now increased to 100º C by placing the cylinder in contact with a bath containing boiling water. The volume of the gas now becomes V₃. This state of the gas is designated as state C.

(iv) With the cylinder still in contact with the boiling water bath, the pulling force of 60 N on the piston is now withdrawn and the gas is allowed to get compresed to state D.

(v) The gas in the cylinder is now subjected to a certain process in which the piston moves up through a distance of 0.1 m without any change in the pressure of the gas. The gas attains state E after the expansion. Now answer the following:

(a) Calculate the volume (V₁) of the gas in state A

(b) Indicate by putting a tick (√) mark whether the process from state A to state B is adiabatic, isothermal or isobaric

Adiabatic____ Isothermal_____ Isobaric____

Justify your answer

(c) Calculate the pressure of the gas in state C.

(d) Between which states work is done on the gas? Indicate by tick mark:

A to B____ B to C____ C to D____ D to E____

Justify your answer.

(e) Calculate the work done when the gas changes its state from D to E as mentioned in (v) above.

Try to answer the above questions which carry 10 points each. You can take about 11 minutes for answering each question.

I’ll be back soon with model answers for your benefit.