Question

Calculate the heat energy required to melt 4kg of ice when the specific latent heat of fusion of water is 334,000 J/kg.

Answer 1

$\bold{\huge{\blue{\underline{ Solution}}}}$

We have given in the question that,

• 4kg of ice melts at the specific latent heat of fusion of water is 334,000 J/kg .

We know that,

Amount of heat required = Mass * specific heat * change in temperature

[ Specific Latent heat of fusion is the amount of heat required to change one mole of substance from solid to liquid phase without changing in temperature .]

But, For complete melting of substance without change in temperature

Amount of heat required = Mass * Specific latent heat of fusion

Subsitute the required values,

$\sf{\red{ Q = MCl}}$

Where,

• Q = Amount of heat required
• M = Mass of the substance
• Cl = Specific latent heat

Now,

$\sf{ Q = 4 × 334000}$

$\sf{ Q = 1336000 J }$

$\sf{ Q = 1336 KJ }$

Hence, The amount of heat required to melt 4kg ice is 1336KJ

$\bold{\red{ Option\: A \:is\: correct }}$

Answer 2

Taking into account the definition of calorimetry and latent heat, the heat energy required to melt 4 kg of ice when the specific latent heat of fusion of water is 334,000 $\frac{J}{kg}$ is 1,336 kJ.

Calorimetry

Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.

Latent heat

Latent heat is defined as the energy required by a quantity of substance to change state.

When this change consists of changing from a solid to a liquid phase, it is called heat of fusion and when the change occurs from a liquid to a gaseous state, it is called heat of vaporization.

The heat Q that is necessary to provide for a mass m of a certain substance to change phase is equal to

Q = m×L

where L is called the latent heat of the substance and depends on the type of phase change.

Heat energy required to melt ice

In this case, you know:

• m= 4 kg
• L= specific latent heat of fusion of water= 334,000 $\frac{J}{kg}$

Replacing in the expression for latent heat:

Q = 4 kg× 334,000 $\frac{J}{kg}$

Solving:

Q= 1,336,000 J= 1,336 kJ (being 1,000 J= 1 kJ)

Finally, the correct answer is the first option: the heat energy required to melt 4 kg of ice when the specific latent heat of fusion of water is 334,000 $\frac{J}{kg}$ is 1,336 kJ.

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