A 50.0 g block of copper whose temperature is 400 K is placed in an insulating box with a 100

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A 50.0 g block of copper whose temperature is 400 K is...

A 50.0 g block of copper whose temperature is $400 \mathrm{~K}$ is placed in an insulating box with a $100 \mathrm{~g}$ block of lead whose temperature is $200 \mathrm{~K}$. (a) What is the equilibrium temperature of the twoblock system? (b) What is the change in the internal energy of the system between the initial state and the equilibrium state? (c) What is the change in the entropy of the system? (See Table $18-3 .)$

Key Concepts

Thermal Equilibrium

Thermal equilibrium is the state in which all parts of a system reach a uniform temperature, resulting from the exchange of heat until no net heat flow occurs between objects. In an isolated system with no external energy exchange, the final equilibrium temperature is determined by balancing the heat lost by the warmer object with the heat gained by the cooler object.

Conservation of Energy

The principle of conservation of energy states that energy can neither be created nor destroyed, only transformed or transferred. In the context of thermal interactions, this means that the total energy lost by one part of the system (such as a hot object) must equal the total energy gained by another (such as a cold object), assuming no energy escapes the system.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates the amount of heat required to change the temperature of a unit mass of the substance by one degree. This concept is crucial for calculating both the equilibrium temperature and the individual heat transfers, as it allows comparisons of how different materials respond to the same amount of energy change.

Internal Energy

Internal energy refers to the total energy contained within a system, including both the kinetic and potential energies of its molecules. In an isolated system undergoing a heat exchange process, while heat moves between different parts, the overall internal energy of the system remains constant due to conservation of energy.

Entropy

Entropy is a measure of the disorder or randomness in a system and reflects the number of ways a system's energy can be distributed. In thermodynamic processes, particularly in irreversible processes like spontaneous heat flow, the entropy of an isolated system always increases, indicating the direction and irreversibility of these processes.

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