## Ideal gases problems

(Ideal gas constant (R) = 8.3 mol

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 15

2. A gas has a volume of 64 cm

3. When it is fully inflated with hydrogen gas a balloon has a radius of 12 m at a temperature of 20

4. An ideal gas undergoes isothermal expansion at 0 °C from 0.010 m

(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 m

Assuming that the air may be treated as an ideal gas of molar mass 29x10

^{-1}K^{-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 15

^{o}C. What is the true pressure when the reading is 75.5 and the temperature 6^{o}C?2. A gas has a volume of 64 cm

^{3}at 0^{o}C and 88 cm^{3}at 100^{o}C. 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 20

^{o}C. It was filled from gas in cylinders which had a volume of 25 m^{3}at 10^{o}C. If the final pressure in the balloon was 10^{5}Pa, what was the pressure of the gas in the cylinders?4. An ideal gas undergoes isothermal expansion at 0 °C from 0.010 m

^{3}to 0.200 m^{3}. 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 m

^{3}of hot air at atmospheric pressure (10^{5}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.