A rigid tank of small mass contains 40.0 g of argon, initially at 200^∘ C and 100 kPa . The tank

step 1 In this question, we have a rigid tank of small mass containing 40 grams of agon. The initial st

A rigid tank of small mass contains 40.0 g of argon,...

A rigid tank of small mass contains 40.0 $\mathrm{g}$ of argon, initially at $200^{\circ} \mathrm{C}$ and 100 $\mathrm{kPa}$ . The tank is placed into a reservoir at $0^{\circ} \mathrm{C}$ and allowed to cool to thermal equilibrium. (a) Calculate the volume of the tank. (b) Calculate the change in internal energy of the argon. (c) Calculate the energy transferred by heat. (d) Calculate the change in entropy of the argon. (e) Calculate the change in entropy of the constant-temperature bath.

Key Concepts

Ideal Gas Law

The ideal gas law is a fundamental relation in thermodynamics that links pressure, volume, temperature, and the number of moles of a gas through the equation PV = nRT. It serves as the basis for determining the state properties of gases under various conditions and is essential for calculating quantities like the volume of a system given its temperature, pressure, and composition.

Internal Energy of an Ideal Gas

For an ideal gas, the internal energy depends solely on temperature and is independent of pressure or volume. In the case of a monatomic ideal gas, the internal energy can be expressed as U = (3/2)nRT, which means that any change in temperature directly affects the internal energy. This relationship is key when assessing energy changes during heating or cooling processes.

First Law of Thermodynamics

The first law of thermodynamics establishes the principle of energy conservation by stating that the change in the internal energy of a system is equal to the heat added minus the work done by the system (?U = Q - W). In processes where the volume is held constant, such as in a rigid tank, no work is performed (W = 0), making the internal energy change directly equal to the heat transfer.

Entropy Change in Thermodynamic Processes

Entropy is a measure of the disorder or randomness in a system and its change during a process quantifies the degree of irreversibility. For reversible processes, the change in entropy can be calculated using the integral of dQ/T, where dQ is the infinitesimal amount of heat transferred and T is the temperature. Understanding entropy changes is crucial in assessing process spontaneity and the overall efficiency of energy exchanges.

Heat Transfer Calculation

Heat transfer calculations involve quantifying the amount of energy exchanged between a system and its surroundings as heat. In thermodynamic analyses, particularly under constant volume conditions, the connection between heat transfer and changes in internal energy becomes direct, allowing for easier determination of energy exchange and its impact on the system's state.

Constant Volume Process

A constant volume process means that the system's volume does not change during the process. This is significant because it implies that no pressure-volume work is done, and any heat transferred into or out of the system goes directly into changing the system's internal energy. This simplification is very useful in analyzing thermodynamic processes in rigid containers.

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