In: Physics
In the interval between the freezing point (ice point) of water and 700.0deg-C, a platinum resistance thermometer is to be used for interpolating temperatures from 0 °C to the melting point of zinc, 692.666 K. The temperature, in Celcius or Centigrade, is given by a formula for the variation of the resistance of the thermometer with temperature: R = R,o(1 + A Tc + B Tc^2). Ro, A, and B are constants determined by measurements at the ice point, the steam point, and the melting point of zinc. If R equals 12.88350 ohms at the ice point, 88.31639 ohms at the steam point, and 304.28989 ohms at zinc's melting point, find Ro. What is A? What is B?
the resistance of the substance changes with
temperature
as follows
R = R0 (1 + alpha * delta T)
R0 is resistance at 0 0C and R is resistance at temperature difference delta T
according to given data at ice point delta T is zero
so
R = R0(1+0) ==> R at ice point is R0 = 12.88350 ohms
now at steam point delta T = 100 ,
R = R0 (1 + A* delta T)
A = (R/R0-1)/
delta T
=
((88.31639/12.88350)-1) / 100
= 0.05855
/0C
at meltingpoint of zinc 692.666k = 419.516 0c
delt T = 419.516
R = R0(1+B delta T^2)
B = (R/R0-1)/
delta T^2
=
(304.28989/12.88350 - 1) / 419.516^2
B = 0.0001285192
/0C