20. Heat and Temperature

An oblique cylinder is shown. Which of the following expressions correctly represents the volume of the cylinder?

Water’s coefficient of volume expansion in the temperature range from 0°C to about 20°C is given approximately by β = α + bT + cT² , with α = - 6.43 x 10⁻⁵ (C°)⁻¹ , b = 1.70 x 10⁻⁵ (C°)⁻² , and c = -2.02 x 10⁻⁷ ((C°)⁻³. Using the formula for density from Problem 22, show that water has its greatest density at approximately 4.0°C.

Estimate the percent difference in the density of iron at STP, and when it is a solid deep in the Earth where the temperature is 2000°C and under 5000 atm of pressure. Assume the bulk modulus ( 90 x 10⁹ N/m² ) and the coefficient of volume expansion do not vary with temperature and are the same as at STP.

The tube of a mercury thermometer has an inside diameter of 0.140 mm. The bulb has a volume of 0.285 cm³. How far will the thread of mercury move when the temperature changes from 10.5°C to 33.0°C? Take into account expansion of the Pyrex glass.

A storage tank at STP contains 26.5 kg of nitrogen (N₂). What is the volume of the tank?

An aluminum sphere is 8.75 cm in diameter. What will be its % change in volume if it is heated from 30°C to 140°C?

A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 m on a winter day at a temperature of -15°C. How much more interior space does the dome have in the summer, when the temperature is 35°C?

Wine bottles are never completely filled: a small volume of air is left in the glass bottle’s cylindrically shaped neck (inner diameter d = 18.5 mm) to allow for wine’s fairly large coefficient of thermal expansion. The distance H between the surface of the liquid contents and the bottom of the cork is called the “headspace height” (Fig. 17–22), and is typically H = 1.5 cm for a 750-mL bottle filled at 20°C. Due to its alcoholic content, wine’s coefficient of volume expansion is about double that of water; in comparison, the thermal expansion of glass can be neglected. Estimate H if the bottle is kept at 10°C.