## Ideal gases problems

(Ideal gas constant (R) = 8.3 mol-1K-1)

1. A barometer tube 90 cm long contains a small amount of air above the mercury. The barometer reading is 75.0 when the true pressure is 76 cm and the temperature is 15oC. What is the true pressure when the reading is 75.5 and the temperature 6oC?

2. A gas has a volume of 64 cm3 at 0oC and 88 cm3 at 100oC. What value does this give for absolute zero?

3. When it is fully inflated with hydrogen gas a balloon has a radius of 12 m at a temperature of 20oC. It was filled from gas in cylinders which had a volume of 25 m3 at 10oC. If the final pressure in the balloon was 105 Pa, what was the pressure of the gas in the cylinders?

4. An ideal gas undergoes isothermal expansion at 0 °C from 0.010 m3 to 0.200 m3. For 5 moles of gas, calculate:
(a) the work done
(b) the heat added
(c) the change in internal energy.

5. A gas cylinder contains 6.4 kg of oxygen at a pressure of 5 atmospheres. An exactly similar cylinder contains 4.2 kg of nitrogen at the same temperature.

What is the pressure of the nitrogen? (Relative molecular masses: oxygen = 32, nitrogen = 28. Assume that each behaves as a perfect gas.)

6. A hot air balloon when inflated contains 1 500 m3 of hot air at atmospheric pressure (105 Pa). The temperature outside the envelope is 300 K and the mass of the balloon (excluding the hot air) and its passengers is 250 kg.

Assuming that the air may be treated as an ideal gas of molar mass 29x10-3 kgmol-1, find the mean temperature to which the air in the balloon must be heated if the balloon is just to rise.