A 10-L Dewar containing liquid nitrogen (commonly abbreviated as LN2) tips over

Question

A 10-L Dewar containing liquid nitrogen (commonly abbreviated as LN2) tips over in your car while you are transporting it to an ice cream making party. If it completely vaporizes, what volume of nitrogen gas (N 2 ) will be produced at 1 atm and 20C? How does this volume compare to the volume of a typical car interior? Based on your findings, would you recommend transporting liquid N 2 in your car? The density of liquid nitrogen at its normal boiling point (-195.8C) is given in Table A-3a of your text. The normal boiling point is the temperature of boiling at 1 atm pressure. Approximate answer: 7 m 3

Explanation / Answer

The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at 20 °C (68 °F), the speed of sound is 343.2 metres per second (1,126 ft/s). This is 1,236 kilometres per hour (768 mph), or about one kilometer in three seconds or approximately one mile in five seconds. In fluid dynamics, the speed of sound in a fluid medium (gas or liquid) is used as a relative measure of speed itself. The speed of an object (in distance per time) divided by the speed of sound in the fluid is called the Mach number. Objects moving at speeds greater than Mach1 are traveling at supersonic speeds. The speed of sound in an ideal gas is independent of frequency, but it weakly depends on frequency for all real physical situations. It is a function of the square root of the absolute temperature, but is independent of pressure or density for a given ideal gas. Sound speed is slightly dependent on pressure only because air is not quite an ideal gas. In addition, for different gases, the speed of sound is inversely dependent on square root of the mean molecular weight of the gas, and affected to a lesser extent by the number of ways in which the molecules of the gas can store heat from compression, since sound in gases is a type of compression. Although (in the case of gases only) the speed of sound is expressed in terms of a ratio of both density and pressure, these quantities cancel in ideal gases at any given temperature, composition, and heat capacity. This leads to a velocity expression in ideal gases using only the latter independent variables.

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