Final Temperature of Iron and Water After Heat Transfer

In terms of environmental energy management and thermodynamics, understanding the transfer of heat from one substance to another is crucial. This article delves deep into the principles of heat transfer and provides a detailed analysis of how the temperature of a 2 kg piece of iron at 20°C changes after it absorbs 30 kcal of heat and is immediately placed in 1 liter of water at 20°C.

Introduction to Heat Transfer

Heat transfer is a fundamental aspect of thermodynamics, involving the movement of thermal energy from one object to another due to a temperature difference. This movement can occur through conduction, convection, or radiation. In this scenario, we are dealing with conduction, where heat is transferred due to a direct contact between the iron and water.

Initial Data and Given Values

To calculate the final temperature, we need to refer to the following data and values:

Mass of Iron (mFe) 2 kg Initial Temperature of Iron (TIFe) 20°C Heat Added to Iron (QFe) 30 kcal Specific Heat of Iron (cFe) ≈ 0.11 kcal/kg°C Mass of Water (mH2O) 1 kg Initial Temperature of Water (TIH2O) 20°C Specific Heat of Water (cH2O) ≈ 1 kcal/kg°C

Calculation Steps

Step 1: Calculate the Final Temperature of Iron Before Mixing

The heat transfer equation can be written as:

QFe mFe × cFe × (Tf - TIFe)

Rearranging this:

Tf TIFe QFe / (mFe × cFe)

Substituting the values:

Tf 20 30 / (2 × 0.11) 20 30 / 0.22 ≈ 20 136.36 ≈ 156.36°C

This temperature is not realistic as the iron would reach this temperature before the water can take any heat from it.

Step 2: Calculate the Final Temperature of the System

When the iron is dropped into the water, the heat lost by the iron equals the heat gained by the water:

mFe × cFe × (Tf - TIFe) mH2O × cH2O × (Tf - TIH2O)

Substituting the known values:

2 × 0.11 × (Tf - 20) 1 × 1 × (Tf - 20)

This simplifies to:

0.22 × (Tf - 20) Tf - 20

Rearranging the equation:

0.22Tf - 4.4 Tf - 20

20 - 4.4 Tf - 0.22Tf

15.6 0.78Tf

Tf ≈ 15.6 / 0.78 ≈ 20°C

Conclusion

The final temperature of the system after the heat exchange remains approximately 20°C. This conclusion is drawn from the fact that the heat gained by the water exactly compensates for the heat lost by the iron, resulting in no net change in temperature.

Understanding this principle is crucial for a variety of applications in environmental energy management, engineering, and basic thermodynamics studies. By knowing how to calculate the final temperature, you can better manage energy distribution and ensure efficient use of resources in various thermal systems.