How much heat is needed to melt 1.5kg of ice and then to rise the temperature of the resulting water 500c?
Answers
Answer:
ExplanationThe amount of heat required to melt ice and raise the temperature of water T^oCT
o
C is
Q=mL_f+mc\Delta TQ=mL
f
+mcΔT
Here m=1.5 kgm=1.5kg
L_f=3.33*10^5 J/kgL
f
=3.33∗10
5
J/kg is Latent heat of fusion of ice.
c=4186 J/kg.^oCc=4186J/kg.
o
C is heat capacity of water.
\Delta T=50 ^oC-0^oC=50^oCΔT=50
o
C−0
o
C=50
o
C
So,
Q=(1.50)[3.33*10^5 +(4186)(50)]=8.13*10^5 JQ=(1.50)[3.33∗10
5
+(4186)(50)]=8.13∗10
5
J
Proper Question: How much amount of heat is needed to melt 1.5 kg of ice and then to rise the temperature of the resulting water to 50°C?
Answer: The amount of heat needed to melt 1.5 kg of ice and then to rise the temperature of the resulting water to 50°C is equal to 819 kJ.
Given:
Mass of the ice (m) = 1.5 kg
The Final temperature of the resulting water (T) = 50°C
To Find:
The amount of heat required.
Solution:
The latent heat of fusion for water (L) = 336 J/g
The specific heat capacity of water (c) = 4.2 J g⁻¹ K⁻¹
Mass of the ice (m) = 1.5 kg = 1500 gram
→ The latent heat of fusion (L) of a substance is defined as the amount of heat required to convert a unit mass of that substance from the solid state to the liquid state without any change in the temperature.
→ The amount of heat required to melt the ice (Q₁) = mL
∴ Q₁ = mL
∴ Q₁ = 1500 (336)
∴ Q₁ = 504,000 Joules
∴ Q₁ = 504 kJ
→ The specific heat capacity (c) of a substance is the amount of heat energy required to raise the temperature of the unit mass of the substance by 1°C.
→ The amount of heat required to raise the temperature to 50°C (Q₂):
∴ Q₂ = mcΔT
∴ Q₂ = 1500 ×(4.2)×(50-0)
∴ Q₂ = 315,000 Joules
∴ Q₂ = 315 kJ
∴ The total heat required (Q) = Q₁ + Q₂ = 504 + 315 = 819 kJ.
Therefore the amount of heat needed to melt 1.5 kg of ice and then to rise the temperature of the resulting water to 50°C is equal to 819 kJ.
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