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HW 2 Solutions
Discussion Questions
2.2 Rewrite the two expressions as follows:
(1) adiabatic p 1/V (2) isothermal p 1/V
The physical reason for the difference is that, in the isothermal expansion, energy flows
into the system as heat and maintains the temperature despite the fact that energy is lost
as work, whereas in the adiabatic case, where no heat flows into the system, the
temperature must fall as the system does work. Therefore, the pressure must fall faster in
the adiabatic process than in the isothermal case. Mathematically, this corresponds to
> 1. 2.4 The change in a state function is independent of the path taken between the initial and
final states; hence for the calculation of the change in that function, any convenient path
may be chosen. This may greatly simplify the computation involved and illustrates the
power of thermodynamics.
The following list includes only those state functions that we have encountered in the
first two chapters. More will be encountered in later chapters.
Temperature, pressure, volume, amount, energy, enthalpy, heat capacity, expansion
coefficient, isothermal compressibility, Joule–Thomson coefficient. Exercises
2.1(a) The physical definition of work is dw = F dz [2.5].
In a gravitational field the force is the weight of the object, which is F = mg.
If g is constant over the distance the mass moves, dw may be integrated to give the total
work: = = = = , = : = (65 ) 9.81 (4.0 ) = 2.6 × 10 = 2.6 × 10 : = (65 ) 1.60 (4.0 ) = 4.2 × 10 = 4.2 × 10 2.3(a) 2.4(a) For a perfect gas at constant volume
=
=
,
,=
=
= ×
, =
=
(1.00 ) = 1.33 (400 300 ) )
= (1.00
8.314
w = 0 (constant volume); q = (400 300 ) = 1.25 × 10 = +1.25
= 1.25
0 = +1.25 2.8(a) q = H, since pressure is constant 2.11(a) 2.12(a) 2.15(a) In an adiabatic process, the initial and final pressures are related by (eqn 2.29)
=
Where = = = . ( . )( .
. ) = 1.40 2.16(a) 2.23(a) 2.28(a) 2.31(a) 24.8
1.00 = 3.9 × 10
3.9 × 10 (298) × ln = 8.314
+ = 8.05 × 10 = +8.05 × 10 + 131 = 7.92 × 10 2.33(a) 2.34(a) =(
= , = (15 ) = , = ( ) +7.2
( , ) [
( 75 )=+ = +8.1 , ) = +8.1 Problems
2.4 The virial expression for pressure up to the second coefficient is 2.18 2.22 A function has an exact differential if its mixed partial derivatives are equal. That is,
f (x,y) has an exact differential if 2.24 2.36 = 1 ( 1 )=
( = 1 [ )
1 ×
( ) +( 2 [
) 2.35] ...
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This note was uploaded on 11/16/2011 for the course EMA 4314 taught by Professor Phillpot during the Fall '10 term at University of Florida.
 Fall '10
 Phillpot

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