A helium-filled balloon has a volume of 100 L at 25°C and 900 mmHg. What volume will it have at 180 kPa and 20°C?

1 Answer
Jun 30, 2016

Answer:

The combined gas law holds that #(P_1V_1)/T_1=(P_2V_2)/T_2#

Explanation:

The temperatures are quoted in #"degrees Kelvin"#. Of course, the twist introduced is the pressure value. We know that #1*atm# will support a column of mercury #760*mm# high, and the pressure measurement here is #900*mm#. This is not very realistic, as no one would measure those pressures with a mercury manometer. (Why not? Well. have you ever tried to clean up a mercury spill? Putting mercury under pressure is just asking for trouble.)

Thus #P_1=900*mm*Hg=(900*mm*Hg)/(760*mm*Hg*atm^1)# #=# #1.18*atm#

And #P_2=180*kPa=(180*kPa)/(101.32*kPa*atm^-1)# #=# #1.78*atm#

You now have consistent units, and I leave the calculation as an exercise.