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 (m2−m1)g where m2 is the mass of a volume of ambient air and m1 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 (T2/T1), where T1 is the absolute temperature of the air above the fire and T2 is the absolute temperature of the ambient air.

Express your answer in terms of T1, T2, and g.

a = ?

B)

Rearrange your formula from part A to obtain an expression for T1 as a function of T2 and a.

Express your answer in terms of a, T2, and g.

T1 = ?

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. Choose the best estimation.

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 as a multiple of . Choose the best estimation.

a=0.5g
a=1.5g
a=10g
a=0.2g
D)

Assuming an ambient temperature of 15∘C use your formula and your estimate of a to estimate the temperature of the fire.

Express your answer in kelvins to two significant figures.

Tfire = ?