To determine the change in internal energy of the copper bar as it is heated, we can use the formula for internal energy change, which is related to the mass, specific heat capacity, and the temperature change. The formula is given by:
Formula for Change in Internal Energy
The change in internal energy (ΔU) can be calculated using the equation:
ΔU = m * c * ΔT
Where:
- m = mass of the substance (in kg)
- c = specific heat capacity (in J/kg·°C)
- ΔT = change in temperature (in °C)
Given Values
For the copper bar, we have the following values:
- Mass (m) = 1 kg
- Specific heat capacity (c) = 387 J/kg·°C
- Initial temperature (T1) = 20 °C
- Final temperature (T2) = 50 °C
Calculating the Temperature Change
The change in temperature (ΔT) can be calculated as:
ΔT = T2 - T1
Substituting the values:
ΔT = 50 °C - 20 °C = 30 °C
Calculating the Change in Internal Energy
Now, we can substitute the values into the internal energy change formula:
ΔU = m * c * ΔT
ΔU = 1 kg * 387 J/kg·°C * 30 °C
ΔU = 1 * 387 * 30
ΔU = 11610 J
Final Result
The change in internal energy of the 1 kg bar of copper when heated from 20 °C to 50 °C is 11610 Joules.
Understanding the Implications
This calculation shows how much energy is required to raise the temperature of the copper bar. The specific heat capacity indicates how much energy is needed to change the temperature of a unit mass of a substance by one degree Celsius. In this case, the copper bar requires a significant amount of energy to achieve the temperature increase, reflecting its properties as a good conductor of heat.
