You are a professional golfer, participating in a contest to see who can hit the

Question

You are a professional golfer, participating in a contest to see who can hit the ball the furthest. Would you prefer to play at Pebble Beach, where the atmospheric pressure is 14.7 PSI and the temperature is a comfortable 85 F (29.4 C) or at the Cherry Creek Country Club in Denver, where the atmospheric pressure is 12 PSI and the temperature is a cool 60 F (15.5 C)? Assume the molar mass of air is 29 g/mole. Justify your answer with the appropriate calculations.

What would the temperature at Pebble Beach have to be to match the conditions at Cherry Creek?

Explanation / Answer

In golf, you want to hit the ball further, meaning that the ball must foat the most, i.e. there is a strong force pushing the ball

, this farce is called buyancy, the denser the fluid, the MORE force

therefore, find which density is higher:

Density for ideal gas:

PV = nRT

n m/MW and D = m/V

so

D = P*MW/(RT)

For pebble beach

D = 14.7/14.7 * 29 / (0.082*(29.4+273)) = 1.169505 g/mol

for Denver

D = 12/14.7 * 29 / (0.082*(15.5+273)) = 1.000696 g/mol

therefore, choose Pebble Bach, since it has higher density

Q2.

find T for Pebble beach to have cherry creek conditions:

D2 = D1

D2 =  14.7/14.7 * 29 / (0.082*(x+273))

1.000696 = 14.7/14.7 * 29 / (0.082*(x+273))

x = (14.7/14.7 * 29)/1.000696 /0.082 -273

x = 80.412 °C

T = 80.412 °C

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