Question

Consider two closed systems A and B. System A contains \(3000 \mathrm{kJ}\) of thermal energy at \(20^{\circ} \mathrm{C},\) whereas system \(\mathrm{B}\) contains \(200 \mathrm{kJ}\) of thermal energy at \(50^{\circ} \mathrm{C}\). Now the systems are brought into contact with each other. Determine the direction of any heat transfer between the two systems.

Short answer

Answer: The heat transfer will occur from system B to system A.

Step-by-step solution

Compare the initial temperatures of the two systems

System A has an initial temperature of \(20^{\circ}\mathrm{C}\) and system B has an initial temperature of \(50^{\circ}\mathrm{C}\). In this step, we can see that system B has a higher temperature than system A.

Determine the direction of heat flow

Since system B has a higher temperature than system A, and heat always flows from the region of higher temperature to the region of lower temperature, heat will flow from system B to system A until thermal equilibrium is reached. So, the direction of heat transfer between the two systems will be from system B to system A.

Key concepts

Thermal Equilibrium

The concept of thermal equilibrium plays a fundamental role in understanding the behavior of systems in thermal contact. When two systems are in thermal equilibrium, their temperatures are equal, and there is no net heat transfer between them. This is a desired state for many physical and engineering processes since it represents a condition of stability.

Consider the example of systems A and B from the original exercise. Initially, System A is at a temperature of 20°C, while System B is at 50°C. These two systems, when in contact, will naturally exchange heat to achieve a common temperature - this process is the journey towards thermal equilibrium. The flow of heat will continue until neither system gives up nor absorbs additional thermal energy. This equilibrium state occurs when both systems reach a temperature that is intermediate between the initial temperatures of the two individual systems.

It's important to highlight that thermal equilibrium refers not only to the equality of temperature but also to a state where all other parameters influencing the systems' thermal conditions remain constant. It reflects a balance in thermal properties and is a core principle in not only physics but also in various engineering disciplines, for achieving efficient energy management and understanding natural phenomena.

Second Law of Thermodynamics

The Second Law of Thermodynamics is a fundamental principle that provides deep insight into the direction of heat transfer as well as the flow of energy in the universe. It states that heat energy can spontaneously flow only from an object at a higher temperature to one at a lower temperature, never the reverse, unless external work is applied.

In the context of our exercise, the second law helps predict the heat will transfer from System B (the hotter system at 50°C) to System A (the cooler system at 20°C). This law underpins why a cup of hot coffee will eventually cool down in a colder room rather than getting hotter; the heat flow from the coffee to the room is a natural process. The second law is also responsible for the concept of entropy, which measures the amount of disorder in a system. In any closed system, entropy tends to increase over time, leading to the dispersal of energy and making it less available for doing useful work.

This principle is essential in designing heat engines, refrigerators, and understanding the ultimate fate of all energy transformations. Engineers and scientists design systems by utilizing this law to predict energy efficiency and thermodynamic processes.

Temperature Gradient

A temperature gradient is essentially a physical quantity that represents how temperature changes from one point to another within a material or space. It is the driving force behind the flow of heat from a warmer region to a cooler region.

In our textbook exercise, a temperature gradient is established between System A (at 20°C) and System B (at 50°C) when they are brought into contact. This gradient is what triggers the movement of thermal energy from the hot system to the cold system. The difference in temperatures creates an imbalance that nature seeks to remedy by transferring energy in the form of heat until the temperatures are equalized, thereby eliminating the gradient.

The concept of the temperature gradient is applied in numerous real-life applications, from environmental science, where it explains atmospheric and oceanic phenomena, to engineering, where it guides the design of insulation materials and controls heating and cooling systems. Understanding the dynamics of temperature gradients allows scientists and engineers to predict and control the rate of heat transfer in various contexts.