Question

A hot metal block is plunged into water in a well-insulated container. The temperature of the metal block goes down, and the temperature of the water goes up until their temperatures are the same. A total of \(1500 \mathrm{J}\) of energy is lost by the metal object. By how much did the energy of the water increase? What law of science is illustrated by this problem?

Short answer

The water gains 1500 J of energy. This illustrates conservation of energy.

Step-by-step solution

Understand the Scenario

The problem involves a metal block losing energy as it is cooled in water. Since the container is well-insulated, no energy escapes into the environment, meaning all energy lost by the metal is gained by the water.

Identify the Key Principle

This exercise illustrates the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred. In this scenario, energy lost by the metal is equal to the energy gained by the water.

Apply the Law of Conservation of Energy

Since the problem states that the metal block loses 1500 J of energy, and no energy is lost to the environment, the water gains the exact amount of energy. Therefore, the energy increase of the water is 1500 J.

Key concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. It explains how energy is moved within systems and can help us understand how different processes, such as heating or cooling, can alter a system. In the context of our exercise, thermodynamics helps to describe the energy exchange between the hot metal block and the water. When the block is submerged in water, it cools down because it transfers some of its thermal energy to the water. This process is governed by the principles of thermodynamics, specifically focusing on energy transfer and transformation rather than generation or annihilation of energy.
One important aspect of thermodynamics is the concept of 'systems' and their boundaries. Here, the system comprises the metal block, the water, and the container. Since's the container is well-insulated, it prevents energy from escaping, ensuring all the internal energy transformations can be clearly analyzed.
Thus, thermodynamics provides a framework for understanding these energy exchanges, showing how the energy balance is maintained within the system.

Heat Transfer

Heat transfer is the movement of thermal energy from a hotter object to a cooler one. In our exercise, the metal block is initially hotter than the water. As these two come into contact, heat spontaneously transfers from the hotter block to the cooler water until thermal equilibrium is achieved—or when both temperatures equalize.
There are three main modes of heat transfer: conduction, convection, and radiation. In this situation, conduction is the primary mode. This process occurs directly at the interface of the metal and water, where molecules exchange energy through collisions.
Some important points about heat transfer:

• The greater the temperature difference, the more intense the heat transfer.
• It continues until both objects reach the same temperature.
• A well-insulated system limits heat exchange with the surroundings, supporting internal energy conservation.

Understanding heat transfer helps in predicting how and when a system, like the one in our problem, will reach equilibrium.

Law of Conservation of Energy

The law of conservation of energy is a fundamental principle in physics, stating that energy cannot be created or destroyed. Instead, energy transforms from one form to another or is transferred from one system to another. This law is the key principle behind the exercise involving the metal block and water.
When the metal block is placed in the water, the energy it loses is gained by the water. Because the container is well-insulated, no energy escapes the system, making this process a perfect demonstration of energy conservation. The total energy within the system remains constant, even though it switches forms or locations.
Important aspects of the law of conservation of energy include:

• Energy balance: Input energy minus output energy equals energy change within a system.
• Equivalence: The energy lost by one part is precisely equal to the gain by another.
• An isolated system, like the well-insulated container, is ideal for observing conserving phenomena.

In conclusion, this law guarantees that all energy transferred from the metal to the water is accounted for, maintaining the system's energy integrity.