Problem Set on Heat & Thermodynamics Thermometry 1. The precision & reliability of ‘Modern Platinum Resistance Thermometers’ are due to the work of Callender & Griffiths who, from a wide range of experiments, found that the resistance of ‘Pure Platinum’ is very accurately given by            where      are resistances at    respectively and    are constants of finite dimensions depending upon the material being tested. Also we know that the platinum temperature is calculated from the formula                Show that, using the these two relations, a true temperature  can be measured by the formula:              where  is a constant depending upon the purity of the specimen. 2. A platinum resistance thermometer reads   at    at  and   in a bath. Calculate the temperature of the bath on Platinum scale & Celsius scale. Assume   . 3. The resistances of a Platinum wire at   and at Sulphur point  are found to be        respectively. The resistance of the wire at a temperature  is given by           . Calculate the ratio . 4. The platinum temperature corresponding to  on the gas scale is . find the temperature on the platinum scale that corresponds to  on the gas scale. 5. The resistances of a Platinum wire at   and at Sulphur point  are found to be        respectively. Find the true temperature when the resistance of the thermometer is  . 6. The resistance of a carbon resistor obeys the following relation:           where  is the temperature. The resistance is found to be exactly   in a liquid helium cryostat. If       , what is the temperature of the cryostat? Kinetic Theory of Gases 7. Calculate the pressure exerted by a gas having     molecules per c.c. at a temperature of . 8. Calculate the r.m.s. velocity of hydrogen at NTP. Given that 1 litre hydrogen weighs 0.0897 g at NTP. 9. At what temperature will the r.m.s. velocity of a gas is half of its value at ? 10. The mean kinetic energy of a molecule at  is     erg. Calculate the number of molecules per c.c. of an ideal gas at  and at a pressure of 40 mm of Hg. 11. Estimate the size of a He atom, assuming its mean free path at NTP to be     cm. Given the density of He at NTP is  g/Litre and the mass of He atom is     g. (Hint:      )