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

Options

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

Answer

To solve the problem, we need to analyze the relationships between the Kelvin, Celsius, and Fahrenheit temperature scales.

### Step-by-Step Solution:

1. **Understanding the Temperature Scales**:
- The Kelvin (K) scale is an absolute temperature scale where 0 K is the absolute zero.
- The Celsius (°C) scale is based on the freezing and boiling points of water.
- The Fahrenheit (°F) scale is another temperature scale commonly used in the United States.

2. **Conversion Formulas**:
- The relationship between Celsius and Kelvin is given by:
\[ K = °C + 273.15 \]
- The relationship between Celsius and Fahrenheit is given by:
\[ °F = (°C \times \frac{9}{5}) + 32 \]

3. **Setting Up the Problem**:
- We need to find a temperature where the reading on the Kelvin scale (K) is numerically equal to the reading on the Celsius scale (°C) and also less than the Celsius reading in terms of Fahrenheit (°F).

4. **Analyzing the Options**:
- **Option A**: K = °C (This is not possible because K is always greater than °C).
- **Option B**: K < °C (This is also not possible because K is always greater than °C).
- **Option C**: K = °F (This is possible, but we need to check the numerical values).
- **Option D**: K < 0 (This is not possible as K cannot be negative).

5. **Finding the Correct Temperature**:
- Since K cannot be less than or equal to °C, we focus on the relationship between K and °F.
- To find a temperature where K = °F, we can set:
\[ K = (K - 273.15) \times \frac{9}{5} + 32 \]
- Solving this equation will give us the temperature where K equals °F.

6. **Solving the Equation**:
- Rearranging the equation:
\[ K = \frac{9}{5}(K - 273.15) + 32 \]
- Simplifying this will lead to:
\[ K = \frac{9}{5}K - \frac{9 \times 273.15}{5} + 32 \]
- Collecting like terms and solving for K will yield the specific temperature.

7. **Final Result**:
- After solving the equation, we find that the temperature where K = °F is approximately -40 degrees.