The Formula for Specific Heat

Oct 13, 2025 by pinkandtrash.com 25 views

Introduction

In the realm of chemistry, understanding the specific heat of a substance is crucial in various applications, including thermodynamics and heat transfer. The specific heat of a substance is defined as the amount of heat energy required to raise the temperature of a unit mass of the substance by one degree Celsius (or Kelvin). In this article, we will delve into the concept of specific heat and calculate the specific heat of an unknown substance using the given data.

What is Specific Heat?

Specific heat is a measure of the amount of heat energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is an important property of a substance that helps us understand how it responds to changes in temperature. The specific heat of a substance is typically denoted by the symbol 'c' and is usually expressed in units of joules per gram per degree Celsius (J/g°C) or calories per gram per degree Celsius (cal/g°C).

The Formula for Specific Heat

The formula for specific heat is given by:

c = Q / (m * ΔT)

where:

c is the specific heat of the substance
Q is the amount of heat energy added to the substance
m is the mass of the substance
ΔT is the change in temperature of the substance

Given Data

We are given the following data:

Mass of the substance (m) = 11.5 g
Change in temperature (ΔT) = 18.7°C
Amount of heat energy added (Q) = 2.0 × 10^1 cal

Calculating the Specific Heat

Using the formula for specific heat, we can calculate the specific heat of the unknown substance as follows:

c = Q / (m * ΔT) = (2.0 × 10^1 cal) / (11.5 g * 18.7°C) = (2.0 × 10^1 cal) / (214.15 g°C) = 0.093 cal/g°C

Interpretation of Results

The calculated specific heat of the unknown substance is 0.093 cal/g°C. This value indicates that the substance requires a relatively small amount of heat energy to raise its temperature by one degree Celsius. This is a characteristic of substances with low specific heat capacities, such as metals.

Comparison with Other Substances

To put this value into perspective, let's compare it with the specific heat capacities of some common substances:

Water: 1 cal/g°C
Copper: 0.092 cal/g°C
Aluminum: 0.215 cal/g°C

As we can see, the specific heat of the unknown substance is very close to that of copper, indicating that it may have similar thermal properties.

Conclusion

In conclusion, we have calculated the specific heat of an unknown substance using the given data. The calculated value of 0.093 cal/g°C indicates that the substance has a relatively low specific heat capacity, similar to that of copper. This calculation demonstrates the importance of understanding the specific heat of a substance in various applications, including thermodynamics and heat transfer.

References

[1] Atkins, P. W., & de Paula, J. (2010). Physical chemistry. Oxford University Press.
[2] Chang, R. (2010). Physical chemistry for the life sciences. W.H. Freeman and Company.

Appendix

The following table lists the specific heat values of several substances for reference:

Substance	Specific Heat (cal/g°C)
Water	1
Copper	0.092
Aluminum	0.215
Iron	0.11
Gold	0.031

Note: The specific heat values are approximate and may vary depending on the source.