Calculate the specific latent heat of vaporization of steam of 1.13 x 106J of heat energy is required to convert 15kg of steam to water.

1. Analyze the question

We are given the total heat energy ($Q$) required to change the state of a substance and the mass ($m$) of that substance. We need to find the specific latent heat of vaporization ($L_v$).

• Heat energy ($Q$): $1.13 \times 10^6 \text{ J}$
• Mass ($m$): $15 \text{ kg}$
• Specific latent heat ($L_v$): ?

2. Explain the concept

The specific latent heat of vaporization is the amount of heat energy required to change a unit mass of a substance from liquid to gas (or vice versa) at a constant temperature. The formula is:

To find $L_v$, we rearrange the formula:

3. Show the solution

Substitute the given values into the formula:

First, perform the division:

Now, combine this with the power of 10:

To express this in standard form (scientific notation), move the decimal point two places to the right:

4. Identify the answer

Comparing our result to the options provided: A. $7.53 \times 10^5 \text{ Jkg}^{-1}$ B. $7.53 \times 10^{-2} \text{ Jkg}^{-1}$ C. $7.53 \times 10^4 \text{ Jkg}^{-1}$ D. $7.53 \times 10^{-3} \text{ Jkg}^{-1}$

The calculated value matches Option C.

5. Tip

When dealing with scientific notation in JAMB physics, always check the powers of 10 carefully. A common mistake is miscounting the decimal shift. Remember: moving the decimal to the right decreases the exponent, and moving it to the left increases it. You've got this!