If `H_(C) , H_(K)` and`H_(F)` are heat required to raise the temperature of one gram of water by one degree in Celcius , Kelvin and Fahrenheit temperature scales respectively then :-

Options

A. `H_(K)gtH_(C)gtH_(F)`
B. `H_(F)gtH_(C) gtH_(K)`
C. `H_(K) = H_(C) gt H_(F)`
D. `H_(K) = H_(C) = H_(F)`

Explanation

To solve the problem, we need to establish the relationship between the heat required to raise the temperature of one gram of water by one degree in Celsius (H_C), Kelvin (H_K), and Fahrenheit (H_F).

### Step-by-Step Solution:

1. **Understanding Heat in Different Scales**:
- The heat (H) required to change the temperature of a substance is given by the formula:
\[ H = m \cdot s \cdot \Delta T \]
where \( m \) is the mass, \( s \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

2. **Heat in Celsius (H_C)**:
- For a change of 1 degree Celsius:
\[ H_C = m \cdot s \cdot 1 \]

3. **Heat in Kelvin (H_K)**:
- For a change of 1 Kelvin:
\[ H_K = m \cdot s \cdot 1 \]
- Note that a change of 1 Kelvin is equivalent to a change of 1 degree Celsius. Hence:
\[ H_K = H_C \]

4. **Heat in Fahrenheit (H_F)**:
- For a change of 1 degree Fahrenheit:
\[ H_F = m \cdot s \cdot 1 \text{ degree Fahrenheit} \]
- We need to convert this change into Celsius. The relationship between Fahrenheit and Celsius is given by:
\[ 1 \text{ degree Fahrenheit} = \frac{1}{1.8} \text{ degrees Celsius} = \frac{5}{9} \text{ degrees Celsius} \]
- Therefore:
\[ H_F = m \cdot s \cdot \left(\frac{5}{9}\right) \]

5. **Comparing the Values**:
- From the above calculations, we have:
- \( H_C = m \cdot s \cdot 1 \)
- \( H_K = m \cdot s \cdot 1 \)
- \( H_F = m \cdot s \cdot \frac{5}{9} \)
- Thus, we can conclude:
\[ H_K = H_C > H_F \]

6. **Final Relationship**:
- The final relationship is:
\[ H_K = H_C > H_F \]

### Conclusion:
The relationship between the heat required to raise the temperature of one gram of water by one degree in Celsius, Kelvin, and Fahrenheit is:
\[ H_K = H_C > H_F \]