Calculating the Amount of Heat Required to Fuse a Substance

Oct 13, 2025 by wbrum.org 85 views

**The Melting Temperature of a Body: A Comprehensive Guide** ===========================================================

Introduction

In this article, we will explore the concept of melting temperature and its relation to the amount of heat required to fuse a substance. We will use a specific example to illustrate the calculation of the amount of heat required to fuse 100 g of a substance with a given melting temperature, latent heat, and specific heat.

What is Melting Temperature?

Melting temperature, also known as the melting point, is the temperature at which a substance changes state from solid to liquid. It is an important property of a substance that determines its behavior in different temperature ranges.

What is Latent Heat?

Latent heat is the amount of heat energy required to change the state of a substance from solid to liquid or vice versa. It is a measure of the energy required to break the bonds between the molecules of a substance, allowing it to change its state.

What is Specific Heat?

Specific heat is the amount of heat energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is a measure of the ability of a substance to absorb and release heat energy.

Calculating the Amount of Heat Required to Fuse a Substance

To calculate the amount of heat required to fuse a substance, we need to know its melting temperature, latent heat, and specific heat. We can use the following formula:

Q = mL + mcΔT

Where:

Q is the amount of heat required to fuse the substance
m is the mass of the substance
L is the latent heat of the substance
c is the specific heat of the substance
ΔT is the change in temperature (in this case, the difference between the melting temperature and the initial temperature)

Example: Calculating the Amount of Heat Required to Fuse 100 g of a Substance

Let's use the following values:

Melting temperature: 250 °C
Latent heat: 15 cal/g
Mass: 400 g
Initial temperature: 50 °C
Specific heat: 0.2 cal/g°C

We want to calculate the amount of heat required to fuse 100 g of this substance.

Step 1: Calculate the change in temperature

ΔT = Tm - Ti = 250 °C - 50 °C = 200 °C

Step 2: Calculate the amount of heat required to raise the temperature

Q = mcΔT = 100 g x 0.2 cal/g°C x 200 °C = 4000 cal

Step 3: Calculate the amount of heat required to fuse the substance

Q = mL + mcΔT = 100 g x 15 cal/g + 4000 cal = 1500 cal + 4000 cal = 5500 cal

Therefore, the amount of heat required to fuse 100 g of this substance is 5500 cal.

Q&A

Q: What is the difference between melting temperature and boiling point? A: Melting temperature is the temperature at which a substance changes state from solid to liquid, while boiling point is the temperature at which a substance changes state from liquid to gas.

Q: What is the significance of latent heat in the calculation of the amount of heat required to fuse a substance? A: Latent heat is the amount of heat energy required to change the state of a substance from solid to liquid. It is an important property of a substance that determines its behavior in different temperature ranges.

Q: Can we use the same formula to calculate the amount of heat required to freeze a substance? A: Yes, we can use the same formula to calculate the amount of heat required to freeze a substance. However, we need to use the latent heat of fusion (L) instead of the latent heat of vaporization (L).

Q: What is the unit of specific heat? A: The unit of specific heat is typically expressed in calories per gram per degree Celsius (cal/g°C) or joules per kilogram per degree Celsius (J/kg°C).

Conclusion

In conclusion, the amount of heat required to fuse a substance can be calculated using the formula Q = mL + mcΔT, where Q is the amount of heat required, m is the mass of the substance, L is the latent heat of the substance, c is the specific heat of the substance, and ΔT is the change in temperature. We can use this formula to calculate the amount of heat required to fuse a substance with a given melting temperature, latent heat, and specific heat.