91Ó°ÊÓ

The concept of internal energy change is pivotal in thermodynamics. Internal energy, denoted as \( \Delta U \), represents the total energy contained within a system. It encompasses all forms of energy present, such as kinetic and potential energy of atoms and molecules. For an isolated system, any change in internal energy is zero; however, an open or closed system can have changes, influenced by heat exchange and work. The formula used to calculate the change in internal energy, derived from the First Law of Thermodynamics, is:

• \( \Delta U = \Delta Q - \Delta W \)

where \( \Delta Q \) is the heat supplied to the system and \( \Delta W \) is the work done by the system. In our exercise, the calculation \( 33.472\ \text{kJ} - 6.00\ \text{kJ} = 27.472\ \text{kJ} \) shows the increase in internal energy, signifying energy storage within the system.

Heat conversion is crucial when dealing with different units of energy. Here, heat was originally given in kilocalories (kcal), while the standard thermodynamic calculations often require energy to be expressed in joules (J) or kilojoules (kJ). To convert kilocalories to kilojoules:

• Use the conversion factor: \( 1\ \text{kcal} = 4184\ \text{J} = 4.184\ \text{kJ} \)

Given that the system receives 8.00 kcal, the conversion becomes:

• \( 8.00\ \text{kcal} \times 4.184\ \text{kJ/kcal} = 33.472\ \text{kJ} \)

This ensures that we use consistent units throughout our calculations. Proper unit conversion is essential to maintain accuracy and coherence in thermodynamic problems.

Work done by a system, expressed as \( \Delta W \), is another significant part of understanding energy changes. When a system performs work, it essentially loses some of its energy to the surroundings. In our scenario, the system does 6.00 kJ of work. For clarity, positive work implies energy is leaving the system — it is energy done by the system to the surroundings, such as expansion of gas against a piston. Therefore, the work done in our problem contributes negatively to the internal energy change, as depicted in the First Law equation:

• \( \Delta U = \Delta Q - \Delta W \)

This equation accounts for both heat supplied and work done, ensuring we compute how the internal energy adjusts.

Energy conversion, especially converting between kilocalories and kilojoules, is vital due to the differing units encountered in various scientific contexts. The primary reason for conversion is to adhere to the unit consistency required: using either joules or kilojoules in calculations.Kilocalories, often used in biological and nutritional contexts, must be converted to joules or kilojoules for physical calculations. This conversion helps avoid calculation errors and improves understanding. To convert energy units:

• Remember that \( 1\ \text{kcal} = 4184\ \text{J} = 4.184\ \text{kJ} \)

Using these conversions, we converted 8.00 kcal to 33.472 kJ, which was essential for integrating this value into the broader thermodynamic calculations. Consistent units allow for accurate application of the First Law of Thermodynamics and accurate calculation of energy changes.