Heat Supplied to Copper and Aluminum: Temperature Comparison

When we supply the same amount of heat to 1 kg of copper and 1 kg of aluminum, which material will have a higher temperature? This question delves into the realms of thermodynamics and the specific heat capacities of these two metals.

Understanding Specific Heat Capacity

Specific heat capacity is a measure of the amount of heat energy required to raise the temperature of one unit of mass of a substance by one degree Celsius (or Kelvin). It plays a crucial role in determining how much a material's temperature will change when heat is added or removed.

Specific Heat Capacities of Copper and Aluminum

The specific heat capacity of copper is approximately 0.385 J/g°C or 385 J/kg°C. For aluminum, this value is around 0.897 J/g°C or 897 J/kg°C. These numbers indicate that a substance with a lower specific heat capacity, like copper, will experience a larger temperature change when the same amount of heat is applied compared to a substance with a higher specific heat capacity, such as aluminum.

Calculating Temperature Change

The formula to calculate the temperature change ((Delta T)) when a certain amount of heat (Q) is added is given by:

[ Q mcDelta T ]

Where:

(Q) heat supplied in joules (m) mass in kilograms (c) specific heat capacity in J/kg°C (Delta T) change in temperature in °C

For the same amount of heat supplied to 1 kg of copper and 1 kg of aluminum:

For copper:

[ Delta T_{text{Cu}} frac{Q}{m cdot c_{text{Cu}}} frac{Q}{1 cdot 385} frac{Q}{385} ]

For aluminum:

[ Delta T_{text{Al}} frac{Q}{m cdot c_{text{Al}}} frac{Q}{1 cdot 897} frac{Q}{897} ]

Since the specific heat capacity of copper (385 J/kg°C) is lower than that of aluminum (897 J/kg°C), the same amount of heat (Q) will cause a larger temperature increase in copper than in aluminum.

Conclusion

When the same amount of heat is supplied to 1 kg of copper and 1 kg of aluminum, after the heat is applied, the copper will have a higher temperature than aluminum. This is due to the lower specific heat capacity of copper, which means it can achieve a higher temperature with the same amount of heat energy.

Understanding the Science Behind It

Copper has a lower specific heat than aluminum because it requires less energy to raise its temperature by one degree Celsius. In simple terms, this means that for the same amount of heat, copper will undergo a more significant temperature change compared to aluminum.

The specific heat of a material is a property that determines how much energy is needed to change its temperature. Materials with lower specific heat capacities can absorb more energy for the same temperature increase, leading to a higher temperature for the same amount of heat supplied.

Further Insights

It's important to note that this principle applies not only to 1 kg of copper and aluminum but to any mass of these materials. The relationship between the specific heat capacity and the temperature change is consistent with the formula ( Q mcDelta T ).

Understanding these principles is crucial in various fields such as engineering, physics, and chemistry, where heat transfer and temperature changes play a vital role in understanding material behavior.