Understanding the Change in Internal Energy of a System in Thermodynamics

Introduction

The first law of thermodynamics is a fundamental principle that helps us understand how energy is transferred or converted within a system. This law states that the change in internal energy (ΔU) of a system (Internal Energy) is equal to the heat added to the system (Q) minus the work done by the system (W). This relationship is expressed by the equation: ΔU Q - W. When discussing the change in internal energy, it is crucial to understand both the heat added to the system and the work done by the system, as these factors significantly influence the overall energy state of the system.

The First Law of Thermodynamics

The first law of thermodynamics can be formally stated as:

[ Delta U Q - W ]

In this equation, the change in internal energy (ΔU) is the total energy change within the system. Heat (Q) is the energy added to the system from its surroundings, while work (W) is the energy the system transfers to its surroundings. The signs of Q and W are crucial: if energy is added to the system (heat), Q is positive; if energy is removed from the system (work done by the system), W is positive.

Calculating Change in Internal Energy

Let us consider an example to illustrate the application of this principle. A system absorbs 455 Joules (J) of heat and does 325 Joules of work. To find the change in internal energy (ΔU), we use the following equation: [ Delta U Q - W ] Given: - Q 455 J (Absorbed heat) - W 325 J (Work done by the system) Plugging in these values, we get: [ Delta U 455 J - 325 J 130 J ] Therefore, the change in internal energy of the system is 130 Joules. This means that the system's internal energy has increased by 130 Joules as a result of the heat absorbed and the work done. This calculation can be mentally visualized as similar to a financial transaction: if someone gives you $455 and you spend $325, you would end up with $130 more.

Application and Further Examples

Example 1

Another example from a previous question is as follows: a system absorbs 180 Joules of heat and does 160 Joules of work. Given the same principle, we can substitute the values into the equation: [ Delta U Q - W ] - Q 180 J - W 160 J Substituting these values in, we get: [ Delta U 180 J - 160 J 340 J ] However, this is an incorrect substitution because the work done by the system should be a negative value. Therefore, the correct calculation should be: [ Delta U 180 J - (-160 J) 180 J 160 J 340 J ]

Example 2

In another scenario, a system absorbs 455 Joules of heat and does 325 Joules of work. Following the same principle, where Q is positive and W is negative, the calculation is:

[ Delta U 455 J - (-325 J) 455 J 325 J 130 J ]

Therefore, the change in internal energy (ΔU) is 130 Joules, confirming our initial calculation. This example demonstrates the importance of correctly identifying the signs of Q and W in the equation.

Conclusion

The understanding of the first law of thermodynamics is essential in comprehending how changes in internal energy occur. By applying the equation ΔU Q - W to various scenarios, we can accurately determine the change in internal energy of a system, whether it is from heat absorption or work done. It is crucial to remember that the signs of Q and W play a significant role in calculating the change in internal energy, as they reflect the direction of energy transfer. Whether it is a financial understanding or a physical interpretation, thinking through these problems can provide valuable insights into thermodynamics.