In the figure below, the change in internal energy of a gas that is taken from A
ID: 1377785 • Letter: I
Question
In the figure below, the change in internal energy of a gas that is taken from A to C along the blue path is +815 J. The work done on the gas along the red path ABC is -445 J.
(a) How much energy must be added to the system by heat as it goes from A through B to C?
J
(b) If the pressure at point A is five times that of point C, what is the work done on the system in going from C to D?
J
(c) What is the energy exchanged with the surroundings by heat as the gas goes from C to A along the green path?
J
(d) If the change in internal energy in going from point D to point A is +515 J, how much energy must be added to the system by heat as it goes from point C to point D?
J
Explanation / Answer
the change in internal energy of a gas that is taken from A to C along the blue path is U = +780 J
The work done on the gas along the red path ABC is W = -425 J.
(a)energy must be added to the system by heat as it goes from A through B to C is
Q = U - W since from 1 st law of thermodynamics
= 815 + 445 = 1260 J
(b) the pressure at point A is P ' = 5P
pressure at point C is P = P
the work done on the system in going from C to D is W ' = P * -dV
where dV = change in volume
we know W = P ' * dV
from this dV = W / P '
= -445 / 5P
= -89 / P
So, W ' = P * ( 89 / P ) = 89 J
(c) the energy exchanged with the surroundings by heat as the gas goes from C to A along the green path Q ' = W' - U Since along the path change in internal enenrgy is +ve than in opposite direction it
is -ve
= - 89 J -815 J
= - 904 J
(d) the change in internal energy in going from point D to point A is U ' = +515 J
energy must be added to the system by heat as it goes from point C to point D is
we know change in internal energy from C to D + change in internal enrgy from D to A = -U
change in internal energy from C to D + U ' = -U
change in internal energy from C to D = -U - U '
= -815 -515 -89 J = - 1419 J