Problem 11 - Pearson Physics

Question

Rank Determine the thermal energy changes of systems A through D, described below, and then rank them in order of increasing change in thermal energy. Indicate ties where appropriate. $$ \begin{array}{|c|c|c|c|c|} \hline \text { System } & \mathbf{A} & \mathbf{B} & \mathbf{C} & \mathbf{D} \\\ \hline \boldsymbol{W}(\boldsymbol{J}) & 10 & -10 & 30 & -20 \\ \hline \boldsymbol{Q}(\boldsymbol{J}) & 20 & -20 & -50 & -10 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

Systems B and D tie, followed by C, then A with the largest increase.

Step 1: Identify the Formula

To determine the change in thermal energy \(\Delta E_\text{thermal}\) for each system, we use the formula: \[\Delta E_\text{thermal} = Q + W\]where \(Q\) is the heat added to the system and \(W\) is the work done on the system.

Step 2: Calculate \(\Delta E_\text{thermal}\) for System A

Plug in the values for System A into the formula:\[\Delta E_\text{thermal, A} = 20 \, \text{J} + 10 \, \text{J} = 30 \, \text{J}\]

Step 3: Calculate \(\Delta E_\text{thermal}\) for System B

Plug in the values for System B into the formula:\[\Delta E_\text{thermal, B} = -20 \, \text{J} + (-10) \, \text{J} = -30 \, \text{J}\]

Step 4: Calculate \(\Delta E_\text{thermal}\) for System C

Plug in the values for System C into the formula:\[\Delta E_\text{thermal, C} = -50 \, \text{J} + 30 \, \text{J} = -20 \, \text{J}\]

Step 5: Calculate \(\Delta E_\text{thermal}\) for System D

Plug in the values for System D into the formula:\[\Delta E_\text{thermal, D} = -10 \, \text{J} + (-20) \, \text{J} = -30 \, \text{J}\]

Step 6: Rank the Thermal Energy Changes

Compare the calculated \(\Delta E_\text{thermal}\) values: - System A: 30 J- System B: -30 J- System C: -20 J- System D: -30 JRank them in increasing order of \(\Delta E_\text{thermal}\): - Systems B and D (both -30 J) tied for lowest- System C (-20 J)- System A (30 J) highest

Key Concepts

Thermodynamics

Thermodynamics is a fundamental branch of physics that studies the relationships between heat, energy, and work. These principles are especially crucial when analyzing thermal energy changes. In this context, thermodynamics helps us understand how energy moves and changes form. A key element of thermodynamics is the concept of a "system", which is any part of the universe that is under consideration. A system's boundary defines what matter and energy it can exchange with its surroundings. For example, a gas inside a cylinder can be considered a system. It's important to realize that as heat and work are exchanged, energy conservation is maintained. According to the first law of thermodynamics, the change in a system's internal energy is equal to the heat transferred into the system plus the work done on the system. By understanding these principles, students can better analyze how different systems exhibit changes in thermal energy. Each type of energy transfer (heat and work) contributes differently to the system’s overall energy change.

Heat Transfer

Heat transfer is the process through which thermal energy moves from one place to another due to temperature differences. It can occur in three primary ways: conduction, convection, and radiation. Conduction involves the direct transfer of heat between molecules in a solid object, like a pan on a hot stove. Convection occurs in fluids (liquids and gases) where warmer areas move into cooler areas, as seen in boiling water. Lastly, radiation involves heat transfer through electromagnetic waves, like from the Sun to Earth. Each system described in the given exercise experiences changes in thermal energy because of heat transfer. The term \( Q \) in the formula acknowledges this heat transfer. When \( Q \) is positive, it indicates that heat is being added to the system, increasing its thermal energy. Conversely, when \( Q \) is negative, the system is losing heat, resulting in a drop in thermal energy. This flow of heat directly impacts the system's overall energy balance.

Work Done on a System

Work done on a system is an essential concept in understanding energy changes, especially within the realm of thermodynamics. Work is the energy transferred when a force is applied over a distance. In the context of thermodynamics, work is typically done on or by the system through volume changes. Think of a piston compressing a gas—here, work is done on the system, which affects its energy state. In the formula \( \Delta E_\text{thermal} = Q + W \), \( W \) represents the work done on the system. A positive \( W \) indicates that the system has work done on it, increasing its internal energy. A negative \( W \) suggests the system is doing work on its surroundings, thus losing energy. Understanding how work influences thermal energy changes helps to clarify why systems might gain or lose thermal energy under different conditions. This principle helps explain the varying outcomes seen in systems A through D from the exercise, shedding light on the energy transformations occurring within each system.