18.55. A parcel of air over a campfire feels an upward buoyant force because the heated...
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18.55. A parcel of air over a campfire feels an upward buoyant force because the heated air is less dense than the surrounding air. By estimating the acceleration of the air immediately above a fire, one can estimate the fire's temperature. The mass of a volume V of air is nMair, where n is the number of moles of air molecules in the volume and Mair is the molar mass of air. The net upward force on a parcel of air above a fire is roughly given by (mout - min)g, where mout is the mass of a volume of ambient air and min is the mass of a similar volume of air in the hot zone. (a) Use the ideal-gas law, along with the knowledge that the pressure of the air above the fire is the same as that of the ambient air, to derive an expression for the acceleration a of an air parcel as a function of (Tout/Tin), where Tin is the absolute temperature of the air above the fire and Tout is the absolute tempera- ture of the ambient air. (b) Rearrange your formula from part (a) to obtain an expression for Tin as a function of Tout and a. (c) Based on your experience with campfires, estimate the acceleration of the air above the fire by comparing in your mind the upward trajectory of sparks with the acceleration of falling objects. Thus you can estimate a as a multiple of g. (d) Assuming an ambient temperature of 15C, use your formula and your estimate of a to estimate the temperature of the fire. 18.55. A parcel of air over a campfire feels an upward buoyant force because the heated air is less dense than the surrounding air. By estimating the acceleration of the air immediately above a fire, one can estimate the fire's temperature. The mass of a volume V of air is nMair, where n is the number of moles of air molecules in the volume and Mair is the molar mass of air. The net upward force on a parcel of air above a fire is roughly given by (mout - min)g, where mout is the mass of a volume of ambient air and min is the mass of a similar volume of air in the hot zone. (a) Use the ideal-gas law, along with the knowledge that the pressure of the air above the fire is the same as that of the ambient air, to derive an expression for the acceleration a of an air parcel as a function of (Tout/Tin), where Tin is the absolute temperature of the air above the fire and Tout is the absolute tempera- ture of the ambient air. (b) Rearrange your formula from part (a) to obtain an expression for Tin as a function of Tout and a. (c) Based on your experience with campfires, estimate the acceleration of the air above the fire by comparing in your mind the upward trajectory of sparks with the acceleration of falling objects. Thus you can estimate a as a multiple of g. (d) Assuming an ambient temperature of 15C, use your formula and your estimate of a to estimate the temperature of the fire.
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Exploring Engineering An Introduction to Engineering and Design
ISBN: 978-0123747235
2nd edition
Authors: Philip Kosky, George Wise, Robert Balmer, William Keat
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