What is the gas pressure in this room. Assume that air has a density of about 1.

Question

What is the gas pressure in this room.  Assume that air has a density of about 1.2x10­^-3 gm cm^-3 and is composed primarily of nitrogen molecules each with a mass of 4.7x10^­23 gm.  Assume room temperature is 300 K.  At the center of the Sun, the density is 150 gm cm^­-3 and the temperature is 15 million K (assume the Sun is composed primarily of hydrogen each with a mass of 1.7x10­^-24 gm).  How much larger is the gas pressure in the center of the Sun compared to the gas pressure in the room ?

Explanation / Answer

Using ideal gas Equation

P1*V1/T1 = P2*V2/T2

V1 = M/density = 4.7*10^-23/(1.2*10^-3) = 3.92*10^-20 cm^3

V2 = M/density= (1.7*10^-24)/(150) = 1.13*10^-26 cm^3

P1*3.92*10^-20/(300) = P2*1.13*10^-26/(15*10^6)

P1*1.3*10^-22 = P2*7.53*10^-34

P2/P1 = (1.3*10^-22)/(7.53*10^-34)

P2/P1 = 1.73*10^11

P2 = 1.73*10^11*P1

So pressure in the center of the sun is 1.73*10^11 times larger than the pressure in the room

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