MCQs

1. A gas has a pressure P, volume V and temperature 500 K. The pressure is doubled at constant volume and then the volume is reduced to one quarter at constant pressure. The final temperature of the gas in K is
   a.   125                             
   b.   250                       
   c.   500                       
   d.   1000
2. At constant temperature, the graph of pressure Vs. reciprocal of volume is
   a.   straight line                
   b.   parabola                
   c.   ellipse                   
   d.   circle
3. Boyle’s law is applicable in
   a.   isochoric condition                                        
   b.   isothermal condition
   c.   isobaric condition                                          
   d.   isotonic process
4. At 0 K, which of the following property of gas will be zero?
   a.   K.E.                            
   b.   P.E.                      
   c.   mass                      
   d.   density
5. A box contains n molecules of gas. If the number of molecules is increased to 2n, the pressure of gas will
   a.   become half                                                   
   b.   becomes 4 times
   c.   remain unchanged                                         
   d.   become twice
6. How much should the pressure of a gas be increased to decrease the volume of the gas by 10% at constant temperature?
   a.   10%                            
   b.   9.5%                     
   c.   11.11%                 
   d.   5.11
7. What is the value of PV/T for one mole of ideal gas?
   a.   8.4 cal/molK               
   b.   4.2 cal/molK         
   c.   2 cal/molK            
   d.   none of above
8. A sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule is m. Which of the following expressions gives the density of the gas?
   a.   mkT                            
   b.   Pm/kT                   
   c.   P/kTV                   
   d.   P/kT
9. A sample of oxygen have the same mass, volume and pressure as another sample of hydrogen. The ratio of their temperature will be [latex]T_o/T_H[/latex]?
   a.   4                                 
   b.   8                           
   c.   16                         
   d.   32
10. Pressure of a gas at constant volume is proportional to
    a.   total energy of gas                                          
    b.   average P.E. of molecules
    c.   average K.E. of molecules                             
    d.   total internal energy of gas

Answers

1.b

2.a

3.b

4.a

5.d

6.c

7.c

8.b

9.c

10.c

CONCEPTUAL PROBLEMS

1. How can Kelvin scale, in principle, be designed by the experiment based on ideal gas law? Explain.
2. What physical concept is provided by universal gas constant? Write its unit.
3. On reducing the volume of a gas at constant temperature, the pressure of a gas increases. Why?
4. What is the difference between a real and an ideal gas? Explain on the basis of the hypothesis of the kinetic theory.
5. Do you expect the gas in cooking as cylinder to obey the ideal gas equation?
6. What are the characteristics of a gas to be an ideal?
7. Why does the cycle tube burst sometimes in summer?
8. What does “the kinetic interpretation of temperature” signify? Explain.
9. Explain on the basis of kinetic theory that the pressure of a gas increases with increase of temperature.
10. At a fixed temperature the volume of a vessel in compressed to half. How will the rms speed of the gas in it change?
11. In the kinetic theory of gases, why do we not take into account the changes in gravitational potential energy of the molecule?
12. At absolute zero temperature, why is the kinetic energy zero?
13. Why do you consider an ideal gas while formulating the pressure in the light of kinetic theory of gases?
14. Outline the essential features of the kinetic theory of gases.
15. If the pressure of a gas increases by 10%, what is the percentage decrease in volume if Boyle’s law holds good.

THEOREY BASED PROBLEMS

16. State Boyle’s and Charle’s law and hence obtain the relationship for the combined gas law.
17. Derive an expression for the pressure exerted by an ideal gas on the basis of kinetic theory.
18. What do you mean by ideal gas? Derive PV = mrT, where symbols have usual meanings.
19. How do you distinguish ideal gas and real gas. Derive P = [latex]\rho rT[/latex] where symbol have usual meaning.
20. Derive ideal gas equation on the basis of kinetic theory of a gas.
21. What is perfect gas? Prove that the average kinetic energy of a gas molecule is directly proportional to the absolute temperature of the gas.

NUMERICAL PROBLEMS

1. Air at 273 K and 1.01 x 10⁵ Nm^-2 pressure contains 2.70 x 10²⁵ molecules per cubic meter. How many molecules per cubic meter will there be at a place, where the temperature is 223K and the pressure is 1.33 x 10⁴ Nm^-2? Ans: 4.35 x 10²⁴ molecules/m³
2. The correct inflation of a tyre at 20^oC is 2 kg/cm². After driving several hours, the driver checks the tyres. If the tyre’s temperature is 50^oC, what should be the pressure reading? Ans: 2.2 x 10⁵ Nm^-2
3. The root mean square (rms) speed of a gas molecule is 600 ms^-1 at 50^oC. Calculate the rms speed of the gas at 100^oC. Ans: 644.76 m/s
4. A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m³ of air at a pressure of 3.4 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m³. If the temperature remains constant, what is the final value of the pressure? Ans: 0.95 atm
5. At a pressure of 700 mm of Hg the root mean square speed of the molecules of a gas is 400 ms^-1. What is its density? Ans: 1.785 kgm^-3
6. What is average translational K.E. of a molecular of an ideal gas at a temperature of 27^oC? What is the total random translational kinetic energy of the molecules in 1 mole of this gas? What is the root – mean – square speed of oxygen molecules at this temperature? Ans: 6.21 x 10^-21 J, 3740 J, 484.4 m/s
7. At what temperature will the average speed of oxygen molecule be sufficient so as to escape from the earth? [Escape velocity from the earth is 11.2 km/s and mass of one oxygen molecule is 53.3 x 10^-24 g, Boltzmann constant = 1.38 x 10^-23 Jmol^-1K^-1]. Ans: 1.6 x 10⁵
8. If one wishes to keep a mole of an ideal gas at STP, how big a container he needs? Ans: 22.4 liter
9. Taking the density of nitrogen at STP to 1.251 kgm^-3, find the root mean square velocity of nitrogen molecules at 127^oC? Ans: 596.898 m/s
10. A cylinder of gas has a mass of 10 kg and pressure of 8 atmosphere at 27^oC. When some gas is used in a cold room at – 3^oC, the gas remaining in the cylinder at this temperature has a pressure of 6.4 atmosphere. Calculate the mass of gas used. Ans: 1.1 kg
11. Helium gas occupies a volume of 0.04 m³ at a pressure of 2 x 10⁵ Nm^-2 and temperature 300 K. Calculate the mass of the helium and root mean square speed of its molecules. (Relative molecular mass of helium = 4, molar gas constant = 8.3 Jmol^-1K^-1). Ans: 1.29 x 10^-2 kg, 1366.57 ms^-1
12. Find the rms speed of Nitrogen at NTP. Density of N₂ = 1.29 kg/m³ at NTP. Ans: 484.65 ms^-1
13. Two glass bulbs of equal volume are joined by a narrow tube and are filled with a gas at STP. When one bulb is kept in melting ice and the other is placed in a hot bath, the new pressure is 877.6 mm of Hg. Calculate the temperature of the bath. Ans: 373 K
14. Two bulbs of equal volume are joined by narrow tube and are filled with a gas at S.T.P. When one bulb is kept in melting ice and the other in boiling water, calculate the new pressure of a gas. Ans: 877.65 mm of Hg