Specific heat capacity of water is

Options

A. 4.186 J `g^(-1)K^(-1)`
B. 4186 J `g^(-1)K^(-1)`
C. 41.86 kJ `g^(-1)K^(-1)`
D. 4186 kJ `g^(-1)K^(-1)`

Answer

To determine the specific heat capacity of water, we can follow these steps:

### Step 1: Understand the Definition of Specific Heat Capacity
Specific heat capacity (c) is defined as the amount of heat (Q) required to raise the temperature of a unit mass (m) of a substance by one degree Celsius (or one Kelvin). Mathematically, it can be expressed as:
\[ c = \frac{Q}{m \Delta T} \]
where:
- \( Q \) = heat added (in Joules)
- \( m \) = mass of the substance (in grams)
- \( \Delta T \) = change in temperature (in degrees Celsius or Kelvin)

### Step 2: Identify the Specific Heat Capacity of Water
For water, the specific heat capacity is known to be approximately 4184 Joules per kilogram per degree Celsius (or Joules per gram per degree Celsius). This means that to raise the temperature of 1 gram of water by 1 degree Celsius, it requires 4184 Joules of heat.

### Step 3: Convert Units if Necessary
The specific heat capacity of water can also be expressed in different units. In this case, we can express it as:
\[ c = 4.184 \, \text{J/g°C} \]
This is equivalent to 4184 J/kg°C when converted to kilograms.

### Step 4: Analyze the Given Options
From the options provided:
1. 4.18 J/g°C (incorrect)
2. 4186 J/g°C (correct)
3. 41 J/g°C (incorrect)
4. 4.184 kJ/kg°C (incorrect, as it should be 4.184 kJ/kg°C)

### Conclusion
The specific heat capacity of water is approximately:
\[ c \approx 4184 \, \text{J/g°C} \]
or equivalently:
\[ c \approx 4.184 \, \text{kJ/kg°C} \]