# Final Temperature Calculation: Water and Iron Bar Interaction

Understanding the interaction between different materials and how they affect each other’s temperature is a fundamental aspect of thermodynamics. This principle is often demonstrated in a common scenario where an iron bar is dropped into a dish of water. The question then arises: what will be the final temperature of the system? This article will delve into the calculations and principles behind this phenomenon, using the example of a 600g dish containing 1500g of water at 20 degrees Celsius, and a 100g iron bar at 120 degrees Celsius.

## Understanding the Basics of Heat Transfer

Before we delve into the calculations, it’s important to understand the basic principles of heat transfer. Heat always flows from a hotter body to a cooler one until equilibrium is reached. In our scenario, the iron bar is hotter than the water, so heat will flow from the iron to the water until they reach the same temperature.

## Specific Heat Capacity

The rate at which a substance changes temperature when it absorbs or loses heat is determined by its specific heat capacity. This is the amount of heat per unit mass required to raise the temperature by one degree Celsius. The specific heat capacity of water is 4.18 J/g°C, and that of iron is 0.45 J/g°C.

## Calculating the Final Temperature

To calculate the final temperature, we use the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred. In this case, the heat lost by the iron bar will be equal to the heat gained by the water and dish. This can be represented by the equation:

Q_lost = Q_gained

Where Q is the heat transferred, calculated as the product of mass, specific heat capacity, and change in temperature (Q = mcΔT). For the iron bar, the heat lost is Q_iron = m_iron * c_iron * (T_initial_iron – T_final), and for the water and dish, the heat gained is Q_water_dish = (m_water * c_water + m_dish * c_dish) * (T_final – T_initial_water_dish).

By setting these two equations equal to each other and solving for T_final, we can find the final temperature of the system.

## Conclusion

Understanding the principles of heat transfer and specific heat capacity allows us to calculate the final temperature in a system where heat is exchanged. In our example, the final temperature will be lower than the initial temperature of the iron bar and higher than the initial temperature of the water and dish, as heat flows from the hotter iron to the cooler water and dish until equilibrium is reached.