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Zorluk: ZorTemperature Scales and Thermometric Properties

A platinum resistance thermometer has a resistance of 10 Ω10\,\Omega at the ice point (0∘C0^\circ\text{C}) and 50 Ω50\,\Omega at the steam point (100∘C100^\circ\text{C}). When placed in a warm liquid bath, an uncalibrated digital ohmmeter reads 38 Ω38\,\Omega. If the ohmmeter has a known positive zero error of +4 Ω+4\,\Omega (indicating 4 Ω4\,\Omega above the true resistance), what is the actual temperature of the liquid bath on the absolute scale in kelvins?

  1. 333 K333\,\text{K}Cevap
  2. B
    343 K343\,\text{K}
  3. C
    353 K353\,\text{K}
  4. D
    60 K60\,\text{K}

Cevap

The actual temperature of the liquid bath on the absolute scale is 333 K333\,\text{K}.
Subtracting the zero error of +4 Ω+4\,\Omega from the raw meter reading of 38 Ω38\,\Omega yields the true thermometric resistance of 34 Ω34\,\Omega. Applying the temperature formula θ=Rθ−R0R100−R0×100∘C\theta = \frac{R_\theta - R_0}{R_{100} - R_0} \times 100^\circ\text{C} gives θ=34−1050−10×100=60∘C\theta = \frac{34 - 10}{50 - 10} \times 100 = 60^\circ\text{C}. Converting to absolute temperature gives T=60+273=333 KT = 60 + 273 = 333\,\text{K}.

Adım Adım Çözüm

1
Correct the measured resistance for zero error
True resistance Rθ=38 Ω−4 Ω=34 ΩR_\theta = 38\,\Omega - 4\,\Omega = 34\,\Omega
A positive zero error means the meter reads higher than the true value, so the zero error must be subtracted.
2
Calculate the temperature on the Celsius scale using linear interpolation
θ=Rθ−R0R100−R0×100∘C=34−1050−10×100=2440×100=60∘C\theta = \frac{R_\theta - R_0}{R_{100} - R_0} \times 100^\circ\text{C} = \frac{34 - 10}{50 - 10} \times 100 = \frac{24}{40} \times 100 = 60^\circ\text{C}
The thermometric property varies linearly between the fixed points.
3
Convert the Celsius temperature to the thermodynamic (absolute) Kelvin scale
T=θ+273=60+273=333 KT = \theta + 273 = 60 + 273 = 333\,\text{K}
The conversion from Celsius to Kelvin requires adding 273273 (or 273.15273.15).

Anahtar Kavram

Linear interpolation of thermometric properties with instrument zero error correction
Tahmini Süre:2m 0s
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Temperature Scales and Thermometric Properties

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