**GASES AND THERMODYNAMICS**

**(In all the following problems consider the gases to be ideal)**

**1. You have a cylinder containing 0.1 m**

^{3}of gas at a pressure of 2 x 10^{5}Pa and a temperature of**20**

^{o}C. How many moles of gas are in the cylinder? [R = 8.31 Jmol^{-1}K^{-1}]**2. Two glass bulbs of equal volume are connected by a narrow tube and filled with gas at 20**

^{o}C and 10^{5}Pa. If one of them is put in melting ice (at 0^{o}C) and the other in steam at 100^{o}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 10**

^{5}Pa at a temperature of 20^{o}C.**What is the new pressure at 40**

^{o}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**

**(b) an adiabatic 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**

**(b) an adiabatic change**

**9. Calculate the root mean square velocity of the air molecules at -50**

^{o}C. [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**

^{o}C.**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**

^{o}C (b) 1000^{o}C (c) 100 x 10^{6 o}C (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}