Chapter 1

The density of a certain type of jet fuel is $775 \mathrm{kg} / \mathrm{m}^{3}$. Determine its specific gravity and specific weight.

At \(4^{\circ} \mathrm{C}\) a mixture of automobile antifreeze \((50 \%\) water and \(50 \%\) ethylene glycol by volume ) has a density of \(1064 \mathrm{kg} / \mathrm{m}^{3}\). If the water density is \(1000 \mathrm{kg} / \mathrm{m}^{3}\), find the density of the ethylene glycol.

A mountain climber's oxygen tank contains 1 lb of oxygen when he begins his rip at sea level where the acceleration of gravity is $32.174 \mathrm{ft} / \mathrm{s}^{2}$. What is the weight of the oxygen in the tank when he reaches the top of Mt. Everest where the acceleration of gravity is $32.082 \mathrm{fts}^{2} ?$ Assume that no oxygen has been removed from the tank; it will be used on the descent portion of the climb.

The information on a can of pop indicates that the can contains \(355 \mathrm{mL}\). The mass of a full can of pop is \(0.369 \mathrm{kg}\), while an empty can weighs 0.153 N. Determine the specific weight, density, and specific gravity of the pop and compare your results with the corresponding values for water at \(20^{\circ} \mathrm{C}\). Express your results in SI units.

With the exception of the 410 bore, the gauge of a shotgun barrel indicates the number of round lead balls, each having the bore diameter of the barrel, that together weigh 1 Ib. For example, a shotgun is called a 12 -gauge shotgun if a \(\frac{1}{12}-1 b\) lead ball fits the bore of the barrel. Find the diameter of a 12 -gauge shotgun in inches and millimeters. Lead has a specific weight of \(0.411 \mathrm{lb} / \mathrm{in}^{3}\).

A regulation basketball is initially flat and is then inflated to a pressure of approximately \(24 \mathrm{lb} / \mathrm{in}^{2}\) absolute. Consider the air temperature to be constant at \(70^{\circ} \mathrm{F}\). Find the mass of air required to inflate the basketball. The basketball's inside radius is 4.67 in.

The temperature and pressure at the surface of Mars during a Martian spring day were determined to be \(-50^{\circ} \mathrm{C}\) and \(900 \mathrm{Pa}\). respectively. (a) Determine the density of the Martian atmosphere for these conditions if the gas constant for the Martian atmosphere is assumed to be equivalent to that of carbon dioxide. (b) Compare the answer from part (a) with the density of the Earth's atmosphere during a spring day when the temperature is \(18^{\circ} \mathrm{C}\) and the pressure \(101.6 \mathrm{kPa}(\mathrm{abs})\).

A closed tank having a volume of \(2 \mathrm{ft}^{3}\) is filled with \(0.30 \mathrm{lb}\) of a gas. A pressure gage attached to the tank reads 12 psi when the gas temperature is \(80^{\circ} \mathrm{F}\). There is some question as to whether the gas in the tank is oxygen or helium. Which do you think it is? Explain how you arrived at your answer.

Assume that the air volume in a small automobile tire is constant and equal to the volume between two concentric cylinders \(13 \mathrm{cm}\) high with diameters of \(33 \mathrm{cm}\) and \(52 \mathrm{cm}\). The air in the tire is initially at \(25^{\circ} \mathrm{C}\) and \(202 \mathrm{kPa}\). Immediately after air is pumped into the tire, the temperature is \(30^{\circ} \mathrm{C}\) and the pressure is 303 kPa. What mass of air was added to the tire? What would be the air pressure after the air has cooled to a temperature of \(0^{\circ} \mathrm{C} ?\)

Develop a computer progrem for calculating the density of an ideal gas when the gas pressure in pascals (abs), the temperature in degrees Celsius, and the gas constant in \(\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\) are specified. Plot the density of helium as a function of temperature from \(0^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\) and pressures of \(50,100,150,\) and \(200 \mathrm{kPa}(\mathrm{abs})\).