Define upper fixed point and lower fixed point as used in thermometry
(b) The electrical resistances of the element in a platinum restistance thermometer at 100\(^o\)C, 0\(^o\) and room temperature are 75.000, 63.000 and 64.992 \(\Omega\) respectively. Use these data to determine the room temperature.
(c) (i) State Boyle’s law
(ii) A uniform capillary tube, closed at one end contained dry air trapped by a thread of mecury 8.5 x 10\(^{-2}\)m long. When the tube was held horinzontally, the length of the air column was 5.0 x 10\(^{-2}\)m, when it was held vertically with the closed end downwards, the length was 4.5 x 10\(^{-2}\)m, Determine the value of the atmospheric pressure. [g = 10ms\(^{-2}\), density of mecury = 1.36 x 10\(^4\) kg m\(^{-3}\)]
Explanation
(a) Upper fixed point is the temperature of steam from boiling water at standard atmospheric pressure of 760 mmHg. Lower fixed point is the temperature of pure melting ice.
(b) 75.000 \(\Omega\) - 1000\(o\)C
\(\frac{64.992 - 63.000}{75.000 - 63.000} = \frac{R - 0}{100 - 0}; 64.992 \Omega - R\)
\(\frac{1.992}{12.000 } = \frac{R_1}{100}; 63.000 \Omega - 0^oC\)
\(R_1 = \frac{1992 \times 100}{12.000} = 16.6^oC\)
(c) (i) Boyle's law states that the volume of a fixed unit varies inversely as the pressure provided the temperature remains constant.
(ii) At horizontal position pressure = A.P = H
Gas volume = 4.5 x 10\(^{-2}\) x cross sectional area of the tube A. But PV = Constant (Boyle's law)
H x 5.0 x 10\(^{-2}\) x A = (H + 8.5 x 10\(^{-2}\)) x 4.5 x 10\(^{-2}\) x A
H = \(\frac{8.5 \times 10^{-2} \times 4.5}{0.5} = 0.765mHg\)
A.P = hpg = 0.765 x 1.36 x 10\(^4\) x 10 = 1.04 x 10\(^{5}\)pa