The Heat Energy Needed For 5 Gm Of Aluminium At 20°C To Melt Is Calculated Using The Specific Heat Capacity (C_al = 0.9 KJ/Kg °C) And The Latent Heat (L_m = 397 KJ/Kg). Options: 19.46 KJ, 13.32 KJ, 13.32 KJ, None, 13.5 KJ, 32.

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The Heat Energy Needed for Melting Aluminium: A Calculation

In this article, we will explore the concept of heat energy required to melt a specific amount of aluminium. The calculation involves the use of specific heat capacity and latent heat, two fundamental properties of materials. Understanding these properties is crucial in various fields, including physics, engineering, and materials science.

What is Specific Heat Capacity?

Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). It is an intrinsic property of a material and is denoted by the symbol C. In the case of aluminium, the specific heat capacity is given as 0.9 KJ/Kg °C.

What is Latent Heat?

Latent heat is the amount of heat energy required to change the state of a substance without changing its temperature. For example, when a substance melts, its temperature remains constant, but its state changes from solid to liquid. The latent heat of fusion is the amount of heat energy required to melt a unit mass of a substance. In the case of aluminium, the latent heat of fusion is given as 397 KJ/Kg.

Calculating the Heat Energy Needed to Melt Aluminium

To calculate the heat energy needed to melt 5 gm of aluminium at 20°C, we need to use the following formula:

Q = m × C × ΔT + m × L

where Q is the heat energy required, m is the mass of the substance, C is the specific heat capacity, ΔT is the change in temperature, and L is the latent heat of fusion.

Step 1: Calculate the Change in Temperature

Since the aluminium is at 20°C and we want to melt it, the change in temperature (ΔT) is:

ΔT = T_f - T_i = 660°C - 20°C = 640°C

Step 2: Calculate the Heat Energy Required to Raise the Temperature

Using the formula Q = m × C × ΔT, we can calculate the heat energy required to raise the temperature of the aluminium:

Q = 0.005 kg × 0.9 KJ/Kg °C × 640°C = 2.88 KJ

Step 3: Calculate the Heat Energy Required to Melt the Aluminium

Using the formula Q = m × L, we can calculate the heat energy required to melt the aluminium:

Q = 0.005 kg × 397 KJ/Kg = 1.985 KJ

Total Heat Energy Required

The total heat energy required to melt the aluminium is the sum of the heat energy required to raise the temperature and the heat energy required to melt it:

Q_total = Q + Q = 2.88 KJ + 1.985 KJ = 4.865 KJ

In conclusion, the heat energy needed to melt 5 gm of aluminium at 20°C is approximately 4.865 KJ. This calculation involves the use of specific heat capacity and latent heat, two fundamental properties of materials. Understanding these properties is crucial in various fields, including physics, engineering, and materials science.

The options provided for the heat energy required to melt 5 gm of aluminium at 20°C are:

  • 19.46 KJ
  • 13.32 KJ
  • 13.32 KJ
  • None
  • 13.5 KJ
  • 32

Based on our calculation, the correct answer is none of the above. The heat energy required to melt 5 gm of aluminium at 20°C is approximately 4.865 KJ, which is not among the options provided.