Question

A system undergoes a process consisting of the following two steps: Step 1: The system absorbs \(72 \mathrm{J}\) of heat while \(35 \mathrm{J}\) of work is done on it. Step 2: The system absorbs \(35 \mathrm{J}\) of heat while performing \(72 \mathrm{J}\) of work. Calculate \(\Delta E\) for the overall process.

Short answer

The change in internal energy for the overall process (∆E) is 70 J.

Step-by-step solution

Calculate ∆E for the first step

Using the first law of thermodynamics equation, we can calculate the change in internal energy for the first step by plugging in the values of q1 and w1: ∆E1 = q1 + w1 ∆E1 = 72 J + 35 J ∆E1 = 107 J The change in internal energy for the first step is 107 J.

Calculate ∆E for the second step

Similarly, using the first law of thermodynamics equation, we can calculate the change in internal energy for the second step by plugging in the values of q2 and w2: ∆E2 = q2 + w2 ∆E2 = 35 J + (-72 J) ∆E2 = -37 J The change in internal energy for the second step is -37 J.

Calculate ∆E for the overall process

Now, we will add the change in internal energies of both steps to find the change in internal energy for the overall process: ∆E_total = ∆E1 + ∆E2 ∆E_total = 107 J + (-37 J) ∆E_total = 70 J The change in internal energy for the overall process is 70 J.

Key concepts

Internal Energy

Understanding internal energy is crucial when studying the first law of thermodynamics. It is a key thermodynamic property and represents the total energy contained within a system, encompassing both the kinetic energy of particles in motion and the potential energy of particles due to their position or arrangement.

The internal energy changes when a system interacts with its surroundings. For example, when heat is added to a system, or when work is done on it, the internal energy increases; conversely, when a system loses heat or does work on its surroundings, its internal energy decreases.

During the textbook exercise, the system gained energy through heat absorption and work being done on it, which increased its internal energy by 107 J in the first step. In the second step, although it absorbed heat, the system did more work than the heat it absorbed, resulting in a decrease of internal energy by 37 J.

Thermodynamics

The science of thermodynamics deals with the principles governing energy transformations and the directionality of processes. The first law of thermodynamics, also known as the law of energy conservation, states that energy can neither be created nor destroyed, only transformed from one form to another.

This law has far-reaching implications for studying physical systems and processes. For instance, it describes how engines work, how refrigerators cool, and fundamentals of climate science. In the context of our textbook problem, the first law relates to the energy changes in a system during the two steps of heat and work interactions.

Heat Transfer

Heat transfer is a form of energy exchange between systems or between a system and its environment due to temperature differences. There are three main methods of heat transfer: conduction, convection, and radiation.

In our exercise, the system absorbs heat in both steps, altering its internal energy. Heat absorption indicates a transfer of energy into the system, thereby increasing its internal energy. Step 1 features absorption of 72 J, while Step 2 again witnesses a heat uptake of 35 J. These changes in energy affect the overall internal energy of the system, which is calculated according to the principles of thermodynamics.

Work Done

In thermodynamics, work done refers to energy transfer when a force is applied to move something over a distance. In a thermodynamic context, work done can involve compression or expansion of a gas, or any other mechanical process that involves transferring energy to or from the system.

In our textbook example, work is done on the system in Step 1 (35 J of work) and by the system in Step 2 (72 J of work). These actions oppose each other in terms of energy flow; the former adds energy to the system, whereas the latter removes energy from the system. When calculating the net change in internal energy for the process, the work done on and by the system must be correctly accounted for to ensure accurate results.