## Saturday, 6 September 2014

### GASES AND THERMODYNAMICS PROBLEMS

GASES AND THERMODYNAMICS

(In all the following problems consider the gases to be ideal)
1. You have a cylinder containing 0.1 m3 of gas at a pressure of 2 x 105 Pa and a temperature of
20o C. How many moles of gas are in the cylinder? [R = 8.31 Jmol-1K-1]

2. Two glass bulbs of equal volume are connected by a narrow tube and filled with gas at 20o C and 105 Pa. If one of them is put in melting ice (at 0o C) and the other in steam at 100o C what is the final pressure in the two bulbs?
3. A 200 ml aerosol can is left out in full sun by mistake. If the original pressure in the can was 1.5 x 105 Pa at a temperature of 20o C.
What is the new pressure at 40o C?
4. What is meant by the root mean square velocity?

5. Explain why it is a useful concept

6. What is meant by:
(a) an isothermal change

7. Write down the first law of thermodynamics explaining carefully the meaning of all the symbols that you use.

8. Explain carefully how the first law would be modified for:
(a) an isothermal change

9. Calculate the root mean square velocity of the air molecules at -50oC. [Density of air = 1.2
kgm-3 ]

6. Calculate the root mean square velocity of the molecules in the plasma in a fusion reactor at a temperature of 100 million oC.

7. Calculate the root mean square velocities of the following gases at STP:
(a) carbon monoxide density = 1.25 kgm-3
(b) chlorine        density = 3.21 kgm-3

8. Calculate the root mean square velocity for hydrogen molecules in a gaseous nebula in deep space at a temperature of 3K.
(Mass of a hydrogen atom = 1.67 x 10-27 kg)

9. Find the average translational kinetic energy of a gas molecule at:
(a) 100 oC   (b)  1000 oC   (c) 100 x 106 oC (fusion reaction)

10. If the average translational energy of a gas molecule is:
(a) 1.6 x 10-19 J (1 eV)
(b) 1.6 x 10-16 J (1 keV)
what is its temperature?
11. Two particles undergoing fusion must have an initial energy of about 0.74 MeV. If this is obtained from their kinetic energy calculate the temperature needed for fusion.
(Boltzmann's constant = 1.38 x 10-23 JK-1, 1 eV = 1.6 x 10-19 J)

12. What is the total random kinetic energy of the molecules in 1 mole of an ideal gas at 300 K?

13. The surface of the Sun has a temperature of about 6000 K and consists largely of hydrogen. Find
(a) the r.m.s velocity and
(b) the kinetic energy of a hydrogen atom there.
Mass of hydrogen atom = 1.66x10-27 kg. Boltzmann’s constant = 1.38x10-28 JK-1