What quantity of heat is required to convert 20 g of ice at 0 ºC to water at the same temperature? (Specific latent heat of ice = 336 Jg$^{-1}$)

Analysis

The question asks for the amount of heat energy required to change the state of a substance (ice to water) without a change in temperature. This is a classic phase change problem.

Concept

When a substance changes state (e.g., from solid to liquid) at a constant temperature, we use the formula for Specific Latent Heat:

Where:

• $Q$ = Quantity of heat energy (in Joules, J)
• $m$ = Mass of the substance (in grams, g)
• $L$ = Specific latent heat of fusion (in Jg⁻¹)

Solution

Step 1: Identify the given values

• Mass ($m$) = 20 g
• Specific latent heat of fusion ($L$) = 336 Jg⁻¹

Step 2: Apply the formula

Step 3: Calculate the result

Step 4: Convert to standard form To match the options provided, we express 6720 in scientific notation:

Conclusion

Comparing our result to the given options, $6.72 \times 10^{3} \text{ J}$ corresponds to option C.

Exam Tip

Always check the units! If the specific latent heat were given in J/kg, you would first need to convert the mass from grams to kilograms (divide by 1000). Since the units here were both in grams (Jg⁻¹ and g), you could multiply them directly without conversion.