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When the ice point i and the steam point s were chosen as fixed points with 100 degrees between them in the original Celsius scale, the ideal-gas temperature of the ice point was written
θi = 100/(rs-1)
Where rs = lim (Ps/Pi) at constant V.
(a) Show that the fractional error in Ti produced by an error in r, is very nearly 3.73 times the fractional error in rs, or
dTi/Ti = 3.73 drs/rs.
(b) Any ideal-gas temperature may be written
T = Tir,
Where r = lim (P/Pi) at constant V. Show that the fractional error in T is
dT/T = (dr/r) + 3.73 drs/rs
(c) Now that the single fixed point of the ideal-gas temperature is a universal constant, show that the fractional error in T is
dT/T = dr/r,
where r = lim(P/PTP) at constant V.
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