Question

There is a temperature at which the reading on the kelvin scale is numerically

• A. equal to that on the celsius scale
• B. lower than that on the celsius scale
• C. less than zero
• D. equal to that on the Fahrenheit scale

Answer 1

The correct option is D

equal to that on the Fahrenheit scale

Step 1: Recall conversion relations-

1. Assume, there is a substance $A$. We use it to measure the temperature of the substance in Celsius, Fahrenheit, and Kelvin scales.
2. Let, $T_C$, $T_F$, $T_K$ are the temperature of $A$ on the Celsius, Fahrenheit, and Kelvin scale respectively.
3. According to the conversion formula $$\begin{gathered} T_F=\frac{9}{5}{T}_C+32 \\ {T}_K=T_C+273.15 \end{gathered}$$

Step 2: Analyse the conversion relations-

1. We can see from the conversion relations, that the temperature of the substance $A$ will never be such that the Kelvin scale reading is equal to or less than that on the Celsius scale.
2. The conversion relations can be rewritten as:
3. $$\begin{gathered} T_F=\frac{9}{5}\left(T_K-273.15\right)+32 \\ 5T_F=9T_K-2298.35 \end{gathered}$$
4. Let, the temperature of the substance $A$ be such that, the temperature reading on Fahrenheit and Kelvin scale is the same.
5. Therefore, $T_F=T_K=T\text{(say)}$
6. Using the conversion relation:
7. $$\begin{gathered} 5T=9T-2298.35 \\ 4T=2298.35 \\ T=574.59\text{K} \end{gathered}$$
8. Hence, at temperature, $574.59\text{K}$ the reading on the Fahrenheit scale and Kelvin scale are the same.
9. Thus, the correct option is (d).