AP Free Response Question
2009 B4 Form B
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The cylinder shown below has an open top, and gas is held inside it by a piston of mass
m
and area
A
. The gas is insulated from its surroundings and is initially in equilibrium at volume V
_{i}
. Express all algebraic answers in terms of the given quantities and fundamental constants.
(a) Determine the absolute pressure P
_{i}
of the gas at equilibrium.
The gas is heated by a circuit that contains three resistors, each of known resistance
R
_{0}
, connected in parallel to a power source of emf
. The piston is held fixed so that the gas remains at constant volume while being heated for a period of time
t
.
(b) Determine the resistance of the circuit.
(c) Calculate the change in internal energy of the gas.
After the time
t
, the circuit is disconnected. The piston is then released and the gas is allowed to expand adiabatically until it reaches volume V
_{f}
.
(d) Indicate below whether the temperature increases, decreases, or remains the same during this process. Justify your answer.
_____ Increases
_____ Decreases
_____ Remains the same
(e) The gas is then compressed isothermally to its original pressure and volume. On the axes below, draw a PV diagram for the complete cycle described in this question, labeling V
_{i}
and V
_{f}
on the volume axis.
Topic Formulas
Description
Published Formula
1st Law of Thermodynamics
actual pressure in a fluid
Bernoulli's Equation
buoyancy
capacitors in parallel
capacitors in series
Carnot efficiency
Continuity Equation
efficiency of a heat cycle
electric current
Ideal Gas Law
internal energy of a confined gas
Joule's Law
Kinetic Theory of Gases
mass density
Ohm's Law
pressure
resistance in parallel
resistance in series
resistivity
root-mean-square speed
specific heat of a confined gas
work done by a confined gas
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