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Chapter 9: Problem 58

A \(1.5\)-m-diameter, 4-m-long cylindrical propane tank is initially filled with liquid propane, whose density is \(581 \mathrm{~kg} / \mathrm{m}^{3}\). The tank is exposed to the ambient air at \(25^{\circ} \mathrm{C}\) in calm weather. The outer surface of the tank is polished so that the radiation heat transfer is negligible. Now a crack develops at the top of the tank, and the pressure inside drops to \(1 \mathrm{~atm}\) while the temperature drops to \(-42^{\circ} \mathrm{C}\), which is the boiling temperature of propane at \(1 \mathrm{~atm}\). The heat of vaporization of propane at \(1 \mathrm{~atm}\) is \(425 \mathrm{~kJ} / \mathrm{kg}\). The propane is slowly vaporized as a result of the heat transfer from the ambient air into the tank, and the propane vapor escapes the tank at \(-42^{\circ} \mathrm{C}\) through the crack. Assuming the propane tank to be at about the same temperature as the propane inside at all times, determine how long it will take for the tank to empty if it is not insulated.

Short Answer

Expert verified
Consider the size of the tank, the density of propane, the temperature of the surroundings, and the heat of vaporization at 1 atm in your answer.

Step by step solution

01

Calculate the volume and mass of propane initially in the tank

To do this, first find the volume of the cylindrical propane tank using the given diameter and length, then use the given density of propane to find the mass of propane in the tank: Volume = π(D/2)^2 * L Mass = Volume * Density
02

Calculate the heat transfer per unit time

To do this, use Newton's Law of Cooling. The heat transfer rate, q, can be expressed as: q = h * A * ΔT where h is the heat transfer coefficient (natural convection), A is the surface area of the tank, and ΔT is the temperature difference between the ambient air and the boiling temperature of propane at 1 atm.
03

Calculate the heat transfer needed to vaporize the mass of propane

To calculate the heat transfer needed to vaporize the mass of propane, use the heat of vaporization given: Q = Mass * Heat of Vaporization
04

Calculate the time it will take for the tank to empty

Finally, divide the total heat transfer needed to vaporize the mass of propane by the heat transfer per unit time to find the time it will take for the tank to empty: Time = Q / q

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Most popular questions from this chapter

Hot water is flowing at an average velocity of \(4 \mathrm{ft} / \mathrm{s}\) through a cast iron pipe \(\left(k=30 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot{ }^{\circ} \mathrm{F}\right)\) whose inner and outer diameters are \(1.0\) in and \(1.2\) in, respectively. The pipe passes through a 50 -ft-long section of a basement whose temperature is \(60^{\circ} \mathrm{F}\). The emissivity of the outer surface of the pipe is \(0.5\), and the walls of the basement are also at about \(60^{\circ} \mathrm{F}\). If the inlet temperature of the water is \(150^{\circ} \mathrm{F}\) and the heat transfer coefficient on the inner surface of the pipe is \(30 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2}{ }^{\circ} \mathrm{F}\), determine the temperature drop of water as it passes through the basement. Evaluate air properties at a film temperature of \(105^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) pressure. Is this a good assumption?

A solar collector consists of a horizontal copper tube of outer diameter \(5 \mathrm{~cm}\) enclosed in a concentric thin glass tube of \(9 \mathrm{~cm}\) diameter. Water is heated as it flows through the tube, and the annular space between the copper and glass tube is filled with air at 1 atm pressure. During a clear day, the temperatures of the tube surface and the glass cover are measured to be \(60^{\circ} \mathrm{C}\) and \(32^{\circ} \mathrm{C}\), respectively. Determine the rate of heat loss from the collector by natural convection per meter length of the tube.

In a plant that manufactures canned aerosol paints, the cans are temperature- tested in water baths at \(55^{\circ} \mathrm{C}\) before they are shipped to ensure that they withstand temperatures up to \(55^{\circ} \mathrm{C}\) during transportation and shelving (as shown in Fig. P9-44 on the next page). The cans, moving on a conveyor, enter the open hot water bath, which is \(0.5 \mathrm{~m}\) deep, \(1 \mathrm{~m}\) wide, and \(3.5 \mathrm{~m}\) long, and move slowly in the hot water toward the other end. Some of the cans fail the test and explode in the water bath. The water container is made of sheet metal, and the entire container is at about the same temperature as the hot water. The emissivity of the outer surface of the container is 0.7. If the temperature of the surrounding air and surfaces is \(20^{\circ} \mathrm{C}\), determine the rate of heat loss from the four side surfaces of the container (disregard the top surface, which is open). The water is heated electrically by resistance heaters, and the cost of electricity is \(\$ 0.085 / \mathrm{kWh}\). If the plant operates \(24 \mathrm{~h}\) a day 365 days a year and thus \(8760 \mathrm{~h}\) a year, determine the annual cost of the heat losses from the container for this facility.

Two concentric spheres of diameters \(15 \mathrm{~cm}\) and \(25 \mathrm{~cm}\) are separated by air at \(1 \mathrm{~atm}\) pressure. The surface temperatures of the two spheres enclosing the air are \(T_{1}=350 \mathrm{~K}\) and \(T_{2}=\) \(275 \mathrm{~K}\), respectively. Determine the rate of heat transfer from the inner sphere to the outer sphere by natural convection.

In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why?
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