You are sitting in a gymnasium watching your local high school basketball team.

Question

You are sitting in a gymnasium watching your local high school basketball team. Assume there are 450 people in the gym. If the gym has (constant) dimensions 50m long, 45m wide, 12m tall, find the following: a. The number of air particles in the gym (mass of single air particle is 4.8 times 10^-26 kg, density of air is 1.3 kg/m^3), assuming none leak out from the walls/doors/etc. b. The number of moles of air in the gym. c. The total heat required to raise the temperature by 4 degrees Celsius assuming no het is lost through the walls. a How many joules of heat must each person in the gym radiate away in order for the temperature to rise by that 4 degrees Celsius?

Explanation / Answer

(A) Volume of room = 50 x 45 x 12= 27000 m^3

mass of air = volume x density = 27000 m^3 x 1.3 kg / m^3

m = 35100 kg

number of air particles = (35100) / (4.8 x 10^-26)

= 7.3125 x 10^29 particles

(b) moles = number of particles / NA

= (7.3125 x 10^29) / (6.022 x 10^23)

= 1214297.6 moles Or 1.21 x 10^6 moles

(c) Q = n Cv deltaT

f = 4.878 for air : Cv = fR/2 = 20.278

Q = (1.21 x 10^6) (20.278)(4)

Q = 98.15 x 10^6 J

(d) by each person = (98.15 x 10^6 J) / 450

= 218.1 x 10^3 J Or 218.1 kJ

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