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. (approx= 3963J).
<h3>What is Sensible heat? </h3><h3 />
Sensible heat is defined as the amount of heat that a body absorbs or releases without any changes in its physical state.
Q= c×m×∆T
<h3>
What is Latent heat? </h3><h3 />
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 the latent heat
<h3>-10°C to 0 °C</h3><h3 />
C= specific heat capacity of ice= 2.108 J/gK
M= 10 g
ΔT= T(final)– T(initial) = 0 °C – (-10 °C)= 10 °C= 10 K
Sensitive heat Q(1) = 2.108×10×10
= 210.8J
<h3>Heat needed to melt ice</h3><h3 />
The specific heat of melting of ice is 334 J/g, the heat needed to melt 10 grams of ice is
Q(2) = 10× 334
= 3340J
<h3>0°C to 10 °C</h3><h3 />
C= specific heat capacity of liquid water is 4.187 J/gK
M= 10 g
ΔT= T(final) – T(initial) = 10 °C – 0 °C= 10 °C= 10 K because being a temperature difference, the difference is the same in °C and K.
Q(3) = 4.187×10×10
= 418.7 J.
Total heat required= Q1 + Q2 + Q3
Total heat required= 210.8 J + 3,340 J + 418.7 J
= 3969.5J
Thus, the heat needed to melt 10 gram of ice from temperature-10°C to 10°C is 3969.5. Therefore, option B is correct option.
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