Thread: Stuck on Ideal Gas Law

A weather balloon carries instruments that
measure temperature, pressure, and humidity as
it rises through the atmosphere. Suppose such a
balloon has a volume of 1.2 m 3 at sea level where
the pressure is 1 atm and the temperature is
20 ° C. When the balloon is at an altitude of 11 km
(36,000 ft) the pressure is down to 0.5 atm and the
temperature is about − 55 ° C.
What is the volume of the balloon then?

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Ideal gas law: PV= NRT. where "P" is the pressure, "V" is the volume, "N" is the number of molecules, "R" is a constant, and "T" is the temperature in degrees Kelvin. 20 degrees C is about 20+ 274= 294 degrees K and -55 C is about -55+ 274= 219 degrees K.

You are told that "such a balloon has a volume of 1.2 m 3 at sea level where the pressure is 1 atm and the temperature is 20 ° C."
So (1)(1.2)= (NR)(294).

You are also told that "When the balloon is at an altitude of 11 km (36,000 ft) the pressure is down to 0.5 atm and the temperature is about − 55 ° C." and asked to find the volume.
So (0.5)V= (NR)(219).

Divide that equation by the first:
which reduces to .

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