The quantity of heat required to melt ice of 0.2 kg whose specific latent heat is 3.4 x 10$^5$J/Kg is

Analysis

To solve this problem, we need to calculate the amount of heat energy required to change the state of a substance (ice to water) without changing its temperature. This is a classic application of the principle of latent heat.

Concept

The quantity of heat ($Q$) required to change the state of a substance is given by the formula:

Where:

• $Q$ = Quantity of heat (measured in Joules, J)
• $m$ = Mass of the substance (measured in kilograms, kg)
• $L$ = Specific latent heat of fusion (measured in J/kg)

Solution

Step 1: Identify the given values

• Mass ($m$) = $0.2 \text{ kg}$
• Specific latent heat ($L$) = $3.4 \times 10^5 \text{ J/kg}$

Step 2: Substitute the values into the formula

Step 3: Perform the calculation

Step 4: Express in standard form To match the format of the options, we convert $68,000$ to standard form:

Conclusion

Comparing our result to the provided options, $6.8 \times 10^4 \text{ J}$ corresponds to option A.

Exam Tip

When dealing with latent heat questions, always check the units. If the mass is given in grams, you must convert it to kilograms (divide by 1000) before multiplying by the specific latent heat, as the standard unit for $L$ is J/kg. Also, remember that "latent" means "hidden"—the temperature doesn't rise during this process, it only changes state!