Q4. A child has a fever of 104 °F. What is this in degrees Celsius?
tC = (104 − 32)/1.8 = 72/1.8 = 40 °C.
Q5. Two thermometers use different liquids that remain liquid over the calibration range and are both calibrated at 0 °C and 100 °C. At 50 °C they may read slightly differently. Why?
Each scale assumes its liquid expands uniformly between the fixed points, but different liquids do not expand in exactly the same way with temperature, so their readings can drift apart between the fixed points.
Q6. Express the steam point in kelvin, using T = t + 273.15.
T = 100 + 273.15 = 373.15 K.
Q7. A faulty Celsius thermometer reads 5° in melting ice and 95° in steam at standard pressure. (a) It reads 41° in a bath; what is the true temperature? (b) At what temperature does it read correctly?
(a) (41 − 5)/(95 − 5) = tC/100, so tC = 36 × 100/90 = 40 °C. (b) If it reads x at the true temperature x, (x − 5)/90 = x/100, so 100x − 500 = 90x and x = 50 °C.
Q8. The mercury thread of a thermometer is 2.0 cm long at the ice point and 22.0 cm at the steam point. What is the temperature when it is 8.0 cm long?
(8.0 − 2.0)/(22.0 − 2.0) = tC/100, so tC = 6.0 × 100/20.0 = 30 °C.