Page 127 - Physical Chemistry

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(assumed to be a perfect gas) goes from 324 K and 424 kPa to R3.9 Starting from dU dq dw, derive the expression for
375 K and 115 kPa. (d) S for the process in (c). (e) U, H, and S for a change of state in an ideal gas. Start by assuming the
S for liquid ethanol going from 20°C and 1 atm to 50°C and process is reversible.
1 atm.
R3.10 The air in a certain room is at a pressure of 1.01 bar
R3.3 Find the molar mass of a gas (assumed ideal) if 6.39 g and contains 52.5 kg of N . The mole fractions of gases in dry
2
3
of the gas in a 3450 cm volume at 10°C has a pressure of air are 0.78 for N , 0.21 for O , and 0.01 for other gases (mainly
2
2
0.888 bar. Ar). Find the mass and partial pressure of O in the room
2
(neglect water vapor). Did you have to assume that the air was
R3.4 True or false? (a) S can never be negative in a closed
system. (b) H U P V for every process in a closed sys- an ideal gas?
tem. (c) For an isothermal process in a perfect gas, q must be R3.11 For each of the following processes, state whether
zero. (d) For an isothermal process in a perfect gas, U must be each of q, w, U, and S is positive, negative, or zero. (a) A
zero. (e) S univ must be zero for every reversible process. perfect gas expands adiabatically into vacuum. (b) Ice melts to
(f) Every adiabatic process in a closed system must be an liquid water at 0°C and 1 atm. (c) Water is cooled from 50°C to
isothermal process. (g) Every isothermal process in a closed 20°C at a constant pressure of 1 atm. (d) Two perfect gases each
system must be an adiabatic process. (h) S is zero for every initially at the same T and P are mixed adiabatically at constant
cyclic process. (i) q is zero for every cyclic process. ( j) S is T and P. (e) Benzene is burned in oxygen in a container with
zero for every adiabatic process in a closed system. rigid, adiabatic walls. ( f ) A perfect gas expands reversibly and
isothermally.
R3.5 Give the SI units of (a) mass; (b) density; (c) molar en-
2
tropy; (d) thermal expansivity; (e) ( U/ V) ; ( f ) molar mass; R3.12 For a perfect gas with C a bT c/T , where a,
T P,m
(g) pressure; (h) C . b, and c are certain constants, find expressions for U, H, and
P
S, when n moles of this gas goes from P , T , to P , T .
R3.6 If 2.50 mol of He gas with C 1.5R nearly indepen- 1 1 2 2
V
dent of T goes from 25°C and 1.00 bar to 60°C and 2.00 bar, find R3.13 A gas obeys the equation of state V RTg(P), where
m
whichever of the following quantities can be calculated from the g(P) is a certain function of pressure that is not being specified.
given information: q, w, U, H, S. Assume a perfect gas. Prove that the thermal expansivity of this gas is 1/T.
a
R3.7 If 2.00 mol of ice at 0°C and 1 atm is heated at constant R3.14 If a hot piece of metal is dropped into cold water in an
pressure to give liquid water at 50°C and 1 atm, find q, w, U, insulated container and the system reaches equilibrium at con-
H, and S. Densities of ice and liquid water at 0°C and 1 atm stant pressure, state whether each of the following three quan-
3
3
are 0.917 g/cm for ice and 1.000 g/cm for liquid water. tities is positive, negative, or zero: S of the water, S of the
Specific heats are 4.19 J/(g K) for liquid water, nearly indepen- metal, S of the metal plus S of the water.
dent of T, and 2.11 J/(g-K) for ice at 0°C. The heat of fusion of
R3.15 Findthefollowingdifferentials:(a)d(PV);(b)d(U PV);
ice is 333.6 J/g.
(c) d(P/T).
R3.8 Starting from dw rev PdV, derive the expression for
w for an isothermal reversible process in an ideal gas.