Heat and Temperature 11 The length of mercury column at 30°C is l0. Suppose the length of the mercury column, if it were at 0°C, is l0. Then, IQ = 75 cm- l e - U 1+^Y(30°C)]. By (i) and (ii), U 1 + |y (30°C)] - 75 cm[l * a(30°C)] ... GO [1 + a(30°C)] [1 + | Y (30°C)] - 75 cm [1 + (a - J) (30°C)] - 74-89 cm . • QUESTIONS FOR SHORT ANSWER 3. 4. 1. If two bodies are in thermal equilibrium in one frame, will they be in thermal equilibrium in all frames ? 2. Does the temperature of a body depend on the frame from which it is observed ? It is heard sometimes that mercury is used in defining the temperature scale because it expands uniformly with the temperature. If the temperature scale is not yet defined, is it logical to say that a substance expands uniformly with the temperature ? In defining the ideal gas temperature scale, it is assumed that the pressure of the gas at constant volume is proportional to the temperature T. How can we verify whether this is true or not ? Are we using the kinetic theory of gases ? Are we using the experimental result that the pressure is proportional to temperature ? Can the bulb of a thermometer be made of an adiabatic wall? Why do marine animals live deep inside a lake when the surface of the lake freezes ? 7. The length of a brass rod is found to be smaller on a hot summer day than on a cold winter day as measured 5. 6. by the same aluminium scale. Do we conclude that brass shrinks on heating ? 8. If mercury and glass had equal coefficient of volume expansion, could we make a mercury thermometer in a glass tube ? 9. The density of water at 4°C is supposed to be 1000 kg/m 3 . Is it same at the sea level and at a high altitude ? 10. A tightly closed metal lid of a glass bottle can be opened more easily if it is put in hot water for some time. Explain. 11. If an autompbile engine is overheated, it is cooled by putting water on it. It is advised that the water should be put slowly with engine running. Explain the reason. 12. Is it possible for two bodies to be in thermal equilibrium if they are not. in contact ? 13. A spherical shell is heated. The volume changes according to the equation Ve = V0 (1 + y0). Does the volume refer to the volume enclosed by the shell or the volume of the material making up the shell ? OBJECTIVE I 1. A system X is neither in thermal equilibrium with Y nor with Z. The systems Y and Z (a) must be in thermal equilibrium (b) cannot be in thermal equilibrium (c) may be in thermal equilibrium. 2. Which of the curves in figure (23-Ql) represents the relation between Celsius and Fahrenheit temperatures ? c Figure 23-Ql 3. Which of the following pairs may give equal numerical values of the temperature of a body ? (a) Fahrenheit and kelvin (b) Celsius and kelvin (c) kelvin and platinum. 4. For a constant volume gas thermometer, one should fill the gas at (a) low temperature and low pressure (b) low temperature and high pressure (c) high temperature and low pressure (d) high temperature and high pressure. 5. Consider the following statements. (A) The coefficient of linear expansion has dimension K- 1 . (B) The coefficient of volume expansion has dimension K'\ (a) A and B are both correct. (b) A is correct but B is wrong.