Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat and Temperature
At the ice point ( 0^ C ), the steam point ( 100^ C ), and the zinc point ( 420^ C ), a resistance thermometer reads R = 20.0 , 27.5 , and 50.0 respectively. Given that the resistance changes with temperature according to the relation R_ = R₀(1 + + ^2) , determine the values of R₀ , , and . Here represents the temperature on the Celsius scale.
Options
- A20.0 , 3.8 10⁻³ ^ C ⁻¹ , -5.6 10⁻⁷ ^ C ⁻²
- B27.5 , 3.8 10⁻³ ^ C ⁻¹ , -5.6 10⁻⁷ ^ C ⁻²
- C20.0 , 5.6 10⁻³ ^ C ⁻¹ , -3.8 10⁻⁷ ^ C ⁻²
- D20.0 , 3.8 10⁻³ ^ C ⁻¹ , 5.6 10⁻⁷ ^ C ⁻²
Correct answer
A. 20.0 , 3.8 10⁻³ ^ C ⁻¹ , -5.6 10⁻⁷ ^ C ⁻²
Step-by-step solution
Given the relation R_ = R₀(1 + + ^2) At = 0^ C , R₀ = 20.0 At = 100^ C , R₁₀₀ = 27.5 27.5 = 20.0(1 + 100 + 10000 ) 100 + 10000 = 27.5 20.0 - 1 = 0.375 + 100 = 0.00375 --- (i) At = 420^ C , R₄₂₀ = 50.0 50.0 = 20.0(1 + 420 + 176400 ) 420 + 176400 = 50.0 20.0 - 1 = 1.5 + 420 = 1.5 420 = 1 280 --- (ii) Subtracting equation (i) from equation (ii): 320 = 1 280 - 3 800 320 = 20 - 21 5600 = - 1 5600 = - 1 320 5600 -5.6 10⁻⁷ ^ C ⁻² Substituting the value of in equation (i): = 0.00375 - 100 (- 1 1792000 ) = 0.00375 + 0.00005