Q2.2 The resistance R
R(θ
(θ ) of a thermostat at temperature θ K is given by R
R(θ
(θ ) = α exp(β/θ ).
Given that the resistance at the ice point (θ = 273.15 K) is 9.00 kΩ and the resistance at the steam
point is 0.50 kΩ, find the resistance at 25 °C.
Ans2.2
From the equation


R(θ
R
(θ ) = α exp(β/θ ).
the resistance at the ice point (θ = 273.15 K) is 9.00 kΩ
9 kΩ = α exp(β/273.15 ).

the resistance at the steam point is 0.50 kΩ
0.50 kΩ = α exp(β/373.15 ).
To find the resistance at 25 °C we should be know the value of β and α
18 kΩ = exp(β/273.15 )/ exp(β/373.15 )
Now we use an technical numerically to find the value of β like the fixed point method .
Then we will find β = 2944.2
After that we use the value of β in the one of the above equation to find the value of α
α = 9 kΩ / exp(2944.2/273.15 )
α = 1.86 × 10^−4

the resistance at 25 °C.
R(298.15k) = (1.86 × 10^−4)* exp(2944.2/298.15 )
R(298.15k) = 3.62 kΩ = R(25 °C)