Difficulty: Easy
Correct Answer: T = tc + 273.15
Explanation:
Introduction / Context:
This question relates to basic thermometry and the relationship between the Celsius and Kelvin temperature scales. Kelvin is the SI unit of temperature and is an absolute scale starting at absolute zero, while the Celsius scale is commonly used in daily life and in laboratories. The question asks which equation correctly relates a Kelvin temperature T to the corresponding Celsius temperature tc for the same physical condition, such as the temperature of a sample of water.
Given Data / Assumptions:
The Celsius scale sets the freezing point of water at 0 degrees Celsius and the boiling point at 100 degrees Celsius under standard atmospheric pressure.
The Kelvin scale sets absolute zero at 0 Kelvin and the triple point of water at 273.16 Kelvin.
The size of one degree Celsius is equal to the size of one Kelvin unit.
We assume standard modern definitions of the temperature scales.
Concept / Approach:
The difference between the Kelvin and Celsius scales is purely an offset. Absolute zero is at 0 K, which corresponds to minus 273.15 degrees Celsius. Since the increments are identical, we can convert from Celsius to Kelvin by adding a constant offset. Specifically, T(K) = tc + 273.15. Any other relationship, such as subtracting 273.15 or treating the scales as independent, would conflict with the standard fixed points like the freezing point of water.
Step-by-Step Solution:
Step 1: Recognise that at the freezing point of water, the Celsius temperature is 0 degrees Celsius and the Kelvin temperature is approximately 273.15 Kelvin.
Step 2: Substitute tc = 0 into the candidate formula T = tc + 273.15, giving T = 0 + 273.15 = 273.15 K, which matches the known value.
Step 3: Check the boiling point of water at 100 degrees Celsius. Using T = tc + 273.15 gives T = 100 + 273.15 = 373.15 K, which matches the standard boiling point in Kelvin.
Step 4: If we tried T = tc - 273.15, then at 0 degrees Celsius the temperature would be negative in Kelvin, which contradicts the definition of Kelvin as an absolute scale starting at zero.
Step 5: Therefore, the correct relation between the Kelvin and Celsius temperature scales is T = tc + 273.15.
Verification / Alternative check:
The relationship between these scales is often written explicitly in textbooks as T(K) = 273.15 + t(°C). This is derived from the fact that both scales have equal increments and that 0 K corresponds to minus 273.15 degrees Celsius. Rearranging the relationship between absolute zero and water freezing point gives the same conversion formula. Checking multiple known temperature points, such as room temperature or the triple point of water, confirms consistency with the equation T = tc + 273.15, reinforcing that it is the correct relation.
Why Other Options Are Wrong:
The statement that the Kelvin and Celsius scales are independent is wrong because they are linearly related by a fixed offset and share the same degree size.
The relation T = tc is wrong because it would give the same numerical value for both scales, which is not true; for example, 0 degrees Celsius does not equal 0 Kelvin.
The relation T = tc - 273.15 is wrong because it would yield negative Kelvin values for temperatures near room temperature and at the freezing point of water, contradicting the concept of an absolute temperature scale where Kelvin values cannot be negative.
Common Pitfalls:
A frequent mistake is mixing up the direction of the offset and writing T = tc - 273 instead of T = tc + 273. Another pitfall is forgetting the decimal 0.15 and approximating too roughly; while 273 is often used in rough calculations, 273.15 is more accurate. Students also sometimes confuse Kelvin with Rankine or other temperature scales. Remembering that Kelvin is always numerically higher than Celsius by about 273 for the same physical temperature helps to keep the sign correct.
Final Answer:
The correct relation between Kelvin temperature T and Celsius temperature tc is T = tc + 273.15.
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