Latent heat of 1 gm of steam is 536 cal/gm , then its value in joule/kg is

Options

A. `2.25xx10^(6)`
B. `2.25xx10^(3)`
C. `2.25`
D. None

Answer

To convert the latent heat of steam from calories per gram to joules per kilogram, we can follow these steps:

### Step 1: Understand the Given Data
We are given the latent heat of steam as 536 cal/gm. We need to convert this value into joules per kilogram.

### Step 2: Convert Calories to Joules
We know that:
1 calorie = 4.2 joules.

### Step 3: Convert Grams to Kilograms
Since we are converting from per gram to per kilogram, we need to remember that:
1 gram = 0.001 kilograms (or 10^-3 kg).

### Step 4: Set Up the Conversion
To convert from calories per gram to joules per kilogram, we can use the following relationship:
\[ \text{Latent heat (in joules/kg)} = \text{Latent heat (in cal/gm)} \times \left(\frac{4.2 \text{ joules}}{1 \text{ calorie}}\right) \times \left(\frac{1000 \text{ grams}}{1 \text{ kg}}\right) \]

### Step 5: Substitute the Values
Substituting the given value of latent heat:
\[ \text{Latent heat (in joules/kg)} = 536 \text{ cal/gm} \times 4.2 \text{ joules/cal} \times 1000 \text{ gm/kg} \]

### Step 6: Calculate the Result
Now, we calculate:
\[ \text{Latent heat (in joules/kg)} = 536 \times 4.2 \times 1000 \]
Calculating this:
\[ 536 \times 4.2 = 2251.2 \]
Then,
\[ 2251.2 \times 1000 = 2,251,200 \text{ joules/kg} = 2.25 \times 10^6 \text{ joules/kg} \]

### Final Answer
Thus, the latent heat of 1 gm of steam in joules per kilogram is:
\[ \text{Latent heat} = 2.25 \times 10^6 \text{ joules/kg} \]