Temperature — Set 4

Correct Answer: A. Fahrenheit scale

• **Fahrenheit scale** = Water freezes at 32°F and boils at 212°F (at 1 atm), giving a range of 212 − 32 = 180 equal Fahrenheit divisions between these two points. • **180 vs. 100** — The Celsius scale has 100 divisions between the same fixed points, so 1°C = 1.8°F (or 9/5 °F). • 💡 Wrong-option analysis: Rankine scale: an absolute scale with Fahrenheit-sized degrees; Celsius scale: has 100 equal divisions, not 180; Kelvin scale: also has 100 equal divisions between ice and steam points.

Correct Answer: B. Kelvin is written as K without a degree sign

• **Kelvin is written as K without a degree sign** = By SI convention, the kelvin is a base unit and is written with the symbol K and no degree sign — unlike Celsius (°C) or Fahrenheit (°F). • **SI rule** — This notation was adopted in 1967 by the General Conference on Weights and Measures (CGPM) to distinguish kelvin from degree-based scales. • 💡 Wrong-option analysis: Kelvin is written only in °C form: °C is the symbol for Celsius, not kelvin; Kelvin is written as k with a degree sign: k (lowercase) is the SI prefix for kilo, not the kelvin unit; Kelvin is written as °K with a degree sign: the degree sign is incorrect for kelvin.

Correct Answer: D. 100°C

• **100°C** = Convert kelvin to Celsius by subtracting 273.15: 373 − 273.15 ≈ 99.85°C ≈ 100°C — the boiling point of water at standard pressure. • **373 K ≈ 100°C** — Water boils at 100°C (373 K) under 1 atm; this is the upper fixed point of the Celsius scale. • 💡 Wrong-option analysis: 50°C: would be 323 K; 150°C: would be 423 K; 0°C: would be 273 K (the ice point).

Correct Answer: A. Kelvin scale

• **Kelvin scale** = Gas laws such as Charles' law (V ∝ T) and Gay-Lussac's law (P ∝ T) are valid only when temperature is in kelvin — an absolute scale starting from absolute zero. • **T(K) = t(°C) + 273.15** — Using Celsius in gas law calculations gives incorrect ratios because 0°C ≠ 0 energy, but 0 K does represent zero thermal energy. • 💡 Wrong-option analysis: Celsius scale only: would give wrong proportionality because Celsius zero is not absolute zero; Fahrenheit scale only: also not an absolute scale; Reaumur scale: an obsolete relative scale, not valid for gas laws.

Correct Answer: D. 212°F

• **212°F** = The boiling point of water at standard atmospheric pressure (1 atm) is 212°F on the Fahrenheit scale, corresponding to 100°C. • **32°F to 212°F = 180°F** — The Fahrenheit scale has 180 divisions between freezing (32°F) and boiling (212°F) of water. • 💡 Wrong-option analysis: 32°F: the freezing point of water, not the boiling point; 180°F: the number of Fahrenheit degrees between freezing and boiling, not the boiling point itself; 100°F: corresponds to about 37.8°C, well below the boiling point.

Correct Answer: D. A narrow constriction in the capillary

• **A narrow constriction in the capillary** = A clinical mercury thermometer has a small constriction near the bulb that prevents mercury from flowing back; this locks the maximum reading until the thermometer is shaken down. • **Constriction function** — After measuring, the mercury column breaks at the constriction and remains at the highest reading, allowing the temperature to be noted after removal from the body. • 💡 Wrong-option analysis: A large bulb filled with air: air would not hold a liquid column reading; A metal coil spring inside: springs are used in some mechanical thermometers but not to hold mercury readings; A rotating digital dial: clinical mercury thermometers are not digital.

Correct Answer: B. 20°C

• **20°C** = Using C = (F − 32) × 5/9: (68 − 32) × 5/9 = 36 × 5/9 = 20°C — a comfortable room temperature. • **68°F = 20°C** — This conversion is commonly encountered in weather reports; 68°F is the standard comfortable indoor temperature used in many countries. • 💡 Wrong-option analysis: 30°C: would be 86°F; 10°C: would be 50°F; 40°C: would be 104°F (a high fever in the body).

Correct Answer: C. 0 K

• **0 K** = Absolute zero is defined as 0 on the kelvin scale — it is the theoretical minimum temperature where molecular kinetic energy is at its minimum. • **0 K = −273.15°C = −459.67°F** — All three scales have a value for absolute zero; only on the kelvin scale is it simply 0. • 💡 Wrong-option analysis: 100 K: corresponds to −173.15°C, not absolute zero; −273.15 K: negative kelvin temperatures are undefined — kelvin cannot be negative; 273.15 K: corresponds to 0°C, the ice point.

Correct Answer: D. 300 K

• **300 K** = Convert Celsius to kelvin: 27 + 273.15 ≈ 300 K — a convenient approximation used widely in physics problems. • **27°C = 300 K** — This round number makes 27°C a standard reference temperature in thermodynamic calculations. • 💡 Wrong-option analysis: 273 K: corresponds to 0°C (ice point), not 27°C; 27 K: corresponds to −246.15°C, an extremely low temperature; 246 K: corresponds to −27°C.

Correct Answer: C. C/5 = (F - 32)/9

• **C/5 = (F − 32)/9** = This is the standard temperature conversion formula relating Celsius C and Fahrenheit F, derived from the fact that 100 Celsius degrees span 180 Fahrenheit degrees. • **5:9 ratio** — The ratio of Celsius to Fahrenheit intervals is 5:9; hence 1°C = 9/5°F = 1.8°F. • 💡 Wrong-option analysis: F/5 = (C − 32)/9: this reverses C and F incorrectly; C = F + 32: wrong — the formula involves both scaling and offset; C/9 = (F − 32)/5: this inverts the ratio, giving wrong results.