Taking into account the definition of calorimetry, sensible heat and latent heat, the heat needed to melt 10.0 grams of ice at -10°C until it is water at 10°C is 3,969.5 J.
Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.
Sensible heat is defined as the amount of heat that a body absorbs or releases without any changes in its physical state (phase change).
In this case, the amount of heat a body receives or transmits is determined by:
Q = c× m× ΔT
where:
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.
In this case, 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.
First, you have to get the ice from -10°C to 0 °C, which is the melting point. Then you have to melt the ice into liquid water. Now, you have to get the water from 0°C to 10°C.
In this case, you know:
Replacing in the definition of sensible heat:
Q1= 2.108 [tex]\frac{J}{gK}[/tex]× 10 g× 10 K
Solving:
Q1= 210.8 J
In this case, you have to melt the ice into liquid water. Being the specific heat of melting of ice is 334 J/g, the heat needed to melt 10 grams of ice is calculated as:
Q2= 10 grams× 334 J/g
Solving:
Q2= 3,340 J
In this case, you know:
Replacing in the definition of sensible heat:
Q3= 4.187 [tex]\frac{J}{gK}[/tex]× 10 g× 10 K
Solving:
Q3= 418.7J
The total heat required is calculated as:
Total heat required= Q1 + Q2 + Q3
Total heat required= 210.8 J + 3,340 J + 418.7 J
Total heat required= 3,969.5 J
In summary, the heat needed to melt 10.0 grams of ice at -10°C until it is water at 10°C is 3,969.5 J.
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