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Density, Pressure and Temperature

1.
Spy balloon is to be constructed of a material with a mass of 0.5kg. it will be filled with helium and must be able to carry and instrument payload of 50kg at an altitude of 1000m where the density of the air is 1.16 kg/m^3. what mass of helium will be required.

2.
If the temperature of gas (measured in K) is doubled
a-the rms speed of the molecules doubles
b-the rms speed increases bh a factor of 2
c-the average kinetic energy quadruples
d-the average kinetic energy increases by a factor of 2

3.
A 1-liter container of nitrogen gas (N2) at a temperature of 23c is intially at a pressure of 1.25 atm. because of a slow leak the pressure falls to 1.15 atm 1 hour later what is the leak rate in molecules/second?

4.
How much energy is required to melt a 500cm^3 block of lead intitially at a temperature of 20c?

Solution Preview

1) As long as the mass of helium plus balloon and the payload is lighter than the air it displaces , the balloon will float in air.

Let mass of helium = m
Combined mass = 50 + 0.5 + m kg
Height = 1000 m

Mass of Helium in the balloon = Volume of Helium in the balloon at 1000 m * density of air at 1000 m

= ( mass / density of Helium) * density of air

Helium weighs 0.1785 g / liter

Using the above values the mass ...

Solution Summary

The solution solves 4 questions on density, mass, temperature and pressure in an attached Word document with calculations shown.

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