What is the specific volume of castor oil of density `956 kgm^(-3)`?

Options

A. `1.05xx10^(-3)kgm^(-3)`
B. `1.05xx10^(-3)m^(3)kg^(-1)`
C. `1.25xx10^(-3)kg^(-1)`
D. `9.56xx10^(-3)kgm^(-3)`

Answer

To find the specific volume of castor oil with a given density of 956 kg/m³, we can follow these steps:

### Step 1: Understand the Concept of Specific Volume
Specific volume is defined as the volume occupied by a unit mass of a substance. It can be mathematically expressed as:

\[ \text{Specific Volume} = \frac{\text{Volume}}{\text{Mass}} \]

### Step 2: Relate Specific Volume to Density
Specific volume is also the reciprocal of density. Therefore, we can express it as:

\[ \text{Specific Volume} = \frac{1}{\text{Density}} \]

### Step 3: Substitute the Given Density
We know the density of castor oil is given as 956 kg/m³. We can substitute this value into the equation for specific volume:

\[ \text{Specific Volume} = \frac{1}{956 \, \text{kg/m}^3} \]

### Step 4: Calculate the Specific Volume
Now, we perform the calculation:

\[ \text{Specific Volume} = \frac{1}{956} \approx 0.00105 \, \text{m}^3/\text{kg} \]

### Step 5: Express in Standard Form
To express the specific volume in standard scientific notation:

\[ \text{Specific Volume} \approx 1.05 \times 10^{-3} \, \text{m}^3/\text{kg} \]

### Conclusion
Thus, the specific volume of castor oil is:

\[ 1.05 \times 10^{-3} \, \text{m}^3/\text{kg} \]

### Final Answer
The correct option is (b) \(1.05 \times 10^{-3} \, \text{m}^3/\text{kg}\).

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