Physics

Physics · thermodynamics

Problem

i. As a parcel of air moves upward, it accelerates. Find a rough estimate for the average speed

v_{0}

during its upward motion. Given constants: b. When the air at the bottom of a container is heated, it becomes less dense than the surrounding air and rises. Simultaneously, cooler air falls downward. This process of net upward heat transfer is known as convection. Consider a closed, rectangular box of height

h

filled with air initially of uniform temperature

T_{0}

. Next, suppose the bottom of the box is heated so that the air there instantly reaches temperature

T_{0}+\Delta T

. The hot parcel of air at the bottom rises upward until it hits the top of the box, where its temperature is instantly reduced to

T_{0}

. You may neglect any heat transfer and friction between the parcel of air and the surrounding air, and assume that the temperature difference is not too large. In addition, you may assume the height

h

is small enough so that the pressure

P_{0}

and density

\rho_{0}

of the surrounding air are very nearly constant throughout the container. More precisely, assume that

\rho_{0} g h / P_{0} \ll \Delta T / T_{0} \ll 1

. Express your answers in terms of

P_{0}, g, h, \Delta T

, and

T_{0}

Related theory

thermodynamics

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