1. The State of a System: The state of a system refers to its condition as described by its
pressure (P), volume (V), temperature (T), and amount of substance (n) or composition (x). The “state” of a simple, pure, homogeneous, chemical system is completely defined by its P, V, and T. Two samples of the same substance are in the same “state” if each has the same P, V, T, and mass.
2. Static pressure: P = F/A. P = pascals (Pa), F = newtons (N), A = square meters (m2).
P = N/m2 = Pa = (kg)(m s–2)/m2 = kg m–1 s–2
Pressure of a Gas: A measure of the average (macroscopic) rate of change of momentum of the molecules or atoms per unit area of wall:
P d(m ) dt A = ( )( / ) ( ) kg m s s m 2 = kg m–1 s–2 = Pa
Pressure Units: 1 standard atmosphere 101 325 Pa = 1.01325 bar = 101.325 kPa = 14.6959 psi (pounds per square inch) = 760 Torr (1 torr = 1 mm Hg).
3. Pascal’s Principle: At any given point in a fluid, the pressure is the same in all direc-
tions. Also, a change P in pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel.
4. The pressure exerted by a column of fluid of density kg m–3 and height z meters is
P = g z where g is the acceleration due to gravity. Standard g = 9.80665 m s–2.
5. Archimedes’ Principle: A body fully or partially immersed in a fluid is buoyed up by
a force equal to the weight of the fluid that the body replaces.
6. Temperature: Celsius scale ( ): 0.00°C is defined as the ice point for water, which is
the temperature at which water saturated with air at one atm pressure is in equilibrium with ice. Kelvin scale (T): Absolute temperature scale. Absolute zero is 0 K. The relationship between the Celsius scale and the Kelvin scale is T = + 273.15.
PROBLEMS
1. The beam balance shown at the right is used to weigh out an amount of NaCl crystals. Exactly enough NaCl is added to the right-hand pan to counterbalance a brass weight placed on the left- hand pan. The brass weight on the left-hand pan has a true weight in vacuum of 100.0000 g. What is the
true weight of the NaCl crystals on the right-hand pan? The densities of air, brass, and crys- talline NaCl are 1.174, 8400, and 2100 kg m–3, respectively.
2. The mass and diameter of a penny are 2.2785 g and 1.90 cm, respectively.
(a) What would be the height of a stack of pennies that generates a static pressure of one atm? (b) How much would this stack of pennies be worth? You may assume that pennies are made of pure copper and that the acceleration due to gravity is constant at 9.806 m s–2.
3. An 80.0 kg man just floats in fresh water with virtually all his body just below the surface. What is his volume if the density of fresh water is 997 kg m–3?
4. An airtight partially evacuated cylindrical container of 10.0 cm inside diameter and inside length 15.0 cm has a lid on the bottom that is held in place by suction. If a mass m of 50.0 kg hanging from the lid is required to break the suction to remove the lid, what is the pressure inside the container? The surroundings are at 25°C and one atm pressure. The mass of the lid may be considered negligible.
5. Estimate the pressure of the atmosphere at an elevation of 5.00 km. For this calculation you may assume that the average temperature of the air is 0°C, the average molar mass of air is
M = 28.8 g mol–1, the acceleration due to gravity is constant at g = 9.806 m s–2, and the pres-
sure at ground level (z = 0) is P = P° = 1.01325 bar. *
6. How many moles of air is contained in a column of air of cross-sectional area 1.00 m2 ex-
tending from the surface of the earth to a height of 1.00 km? For this calculation you may as- sume that the average temperature of the air is 0°C, the average molar mass of air is
M = 28.8 g mol–1, the acceleration due to gravity is constant at g = 9.806 m s–2, and the pres-
sure at ground level (z = 0) is P = P° = 101 325 Pa. * 7. Pascal’s Principle states that any change in pressure ap-
plied to an enclosed incompressible fluid is transmitted undiminished to every part of the fluid as well as to the walls of the container. This is observed when you squeeze a tube of toothpaste. The most common applica- tion of Pascal’s principle is the hydraulic jack, in which a small force applied to a fluid can be used to lift a heavy weight. Thus, consider the following arrangement in which an incompressible fluid such as hydraulic oil is
F1
m
contained in a rigid system containing two pistons. What force F1 is required to lift a mass of
m = 250 kg if the area of the small piston face is A1 = 1.00 cm2 and that of the large piston
face is A2 = 300 cm2?
8. When you are standing, the blood pressure in your upper body is quite different from that in your lower body. Fortunately, the human circulatory system has evolved to solve the prob- lems associated with quickly moving blood through relatively large distances against the force of gravity. Animals such as snakes, eels, and even rabbits, whose circulatory systems have not so adapted, will actually die if held head upward, because their blood pools in their extremities and is unable to reach their brains. When a certain woman stands, her brain is 40 cm higher than her heart; when she bends, it is 35 cm below her heart.
(a) What is the blood pressure in her brain when she is standing? (b) What is the blood pressure in her brain when she is bending over?
Her normal systolic blood pressure––the peak value upon heart contraction––is 120 Torr, while her normal diastolic blood pressure––the value in between beats when the heart relaxes and blood flows from the veins into the heart––is 80 Torr. (This is why the normal blood pressure for a healthy adult is reported as 120/80.) For the purpose of the calculation you may use an average blood pressure; also, any small frictional and velocity effects on blood pressure may be ignored. The density of blood may be taken as 1.0595 g cm–3.
9. The rigid L-shaped tank shown at the right is open at the top and filled with water of density 1000 kg m–3. If the atmospheric pressure is 1.00 bar, what
is the net force exerted by the water on the cross- hatched face of the tank?
10. A glass of water that is filled to the brim contains an ice cube floating at the surface. Taking the buoy- ancy effects of both water and air into account, what would happen to the water level when the ice cube melts if no counteracting surface tension ef- fects were present?
11. A boat of mass m containing a large heavy rock of mass mR, volume VR, and density R floats on a
pond containing a volume of water VW of density W. If the rock is thrown overboard, does the level of the pond rise, fall, or remain the same? Neglect any buoyancy contributions from the air.
12. A blimp is filled with 5000 m3 of helium at 20°C and 1.05 bar pressure. The volume of the
cabin is 30 m3 and the mass of the empty blimp structure (no helium) is 4200 kg. What is the
maximum additional mass m that can be loaded into the cabin and still permit lift off? The surrounding air is at 1.00 bar pressure and 20°C. The molar mass of air is 28.8 g mol–1.
1.5 m 1 m
4 m
1 m
1 m
13. What is the maximum height that water can rise in the pipes of a building if the water pres- sure at the ground floor is 50 psig? Assume the density of water is 0.997 g cm–3.
14. An object of mass m hangs from a spring balance, as shown in the figure at the right. In air, the balance reads 4.00 kg. When the object is immersed in water the balance reads 3.65 kg, and when immersed in an unknown liquid it reads 3.72 kg. What is the density of the unknown liquid? The air (molar mass = 28.8 g mol–1) is at one bar pressure and 25°C. The density of water at
25°C is 0.997 g cm–3.
15. A vertical glass U-tube, open at each end, contains mercury. If 15.0 cm of water is poured into one arm of the tube, by how
much does the level in the other arm rise above its initial level? The densities of water and of mercury can be taken as 0.997 g cm–3 and 13.55 g cm–3, respectively. The atmospheric pres-
sure is 1.024 bar.
16. A piece of wood is floating in a pool of oil with 40.0% of the wood above the surface of the oil. If the oil has a density of 1.25 g cm–3, what is the density of the wood in kg m–3? The
buoyancy contribution from the air may be neglected. The acceleration due to gravity is
g = 9.80 m s–2.