What is the specific latent heat of fusion of ice if it takes 863 kJ to convert 4.6 kg of ice into water at 0 C?
A. $0 J kg -1$
B. $1.87 \times 10^{\wedge} 5 J kg -1$
C. $3969.80 J kg -1$
D. $187.61 J kg -1$
Answer (1)
Define the specific latent heat of fusion formula: Q = m L .
Rearrange the formula to solve for L: $L =
\frac{Q}{m}$.
Convert Q to Joules and substitute the given values: $L =
\frac{863000}{4.6}$.
Calculate the specific latent heat of fusion: $L
\approx 1.87
\times 10^5 J kg^{-1}$.
1.87 × 1 0 5 J k g − 1
Explanation
Problem Introduction We are given that it takes 863 kJ of heat to convert 4.6 kg of ice into water at 0°C. We need to find the specific latent heat of fusion of ice.
Defining the Formula The specific latent heat of fusion (L) is the amount of heat (Q) required to change 1 kg of a solid into a liquid at its melting point. The relationship between these quantities is given by the formula: Q = m L where:
Q is the heat required (in Joules),
m is the mass of the substance (in kg),
L is the specific latent heat of fusion (in J/kg).
Identifying Given Values We are given:
Q = 863 kJ = 863,000 J
m = 4.6 kg We need to find L.
Rearranging the Formula Rearrange the formula to solve for L: L = m Q
Calculating L Substitute the given values into the formula: L = 4.6 kg 863000 J L = 187608.69565217392 J/kg Rounding to two decimal places, we get: L ≈ 1.88 × 1 0 5 J/kg
Choosing the Correct Option Comparing our calculated value with the given options, we see that option B, $1.87
\times 10^5 J kg^{-1}$, is the closest to our calculated value.
Final Answer Therefore, the specific latent heat of fusion of ice is approximately $1.87
\times 10^5 J kg^{-1}$.
Examples
The concept of latent heat is crucial in understanding various real-world phenomena. For instance, it explains why coastal areas have milder climates than inland areas. Water's high latent heat of vaporization means it absorbs a lot of energy when it evaporates, moderating temperatures. Similarly, the latent heat of fusion explains why ice can keep a drink cold for a long time; it absorbs heat from the drink as it melts, rather than immediately raising the water's temperature.
