Consider a system consisting of the following apparatus, in which gas is confined in one flask and there is a vacuum in the other flask. The flasks are separated by a valve. Assume that the flasks are perfectly insulated and will not allow the flow of heat into or out of the flasks to the surroundings. When the valve is opened, gas flows from the filled flask to the evacuated one. (a) Is work performed during the expansion of the gas? (b) Why or why not?

검증된 단계별 안내

Consider the concept of work in thermodynamics, which is defined as the energy transfer that occurs when an object is moved by a force. In the context of gases, work is often associated with a change in volume against an external pressure.

Identify the initial conditions: one flask contains gas, and the other is evacuated, meaning it has no gas and therefore no pressure.

When the valve is opened, the gas expands into the evacuated flask. Since the evacuated flask has no pressure, the gas expands freely without doing work against an external pressure.

Understand that in a free expansion, such as this one, the external pressure is zero, and therefore the work done (W) is calculated as W = P_{ext} \(\times\) \(\Delta\) V, where P_{ext} is the external pressure. Since P_{ext} = 0, the work done is zero.

Conclude that no work is performed during the expansion of the gas because the expansion occurs into a vacuum, where there is no opposing force or pressure to do work against.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Work in Thermodynamics

In thermodynamics, work is defined as the energy transferred when a force is applied over a distance. For gases, work can occur during expansion or compression when the gas exerts pressure on its surroundings. In the context of the question, understanding whether work is done during the gas expansion involves analyzing the system's boundaries and the nature of the expansion process.

Free Expansion

Free expansion refers to the process where a gas expands into a vacuum without performing work on the surroundings. In this scenario, since the gas moves from a filled flask to an evacuated one, there is no opposing pressure to work against, meaning no energy is transferred as work. This concept is crucial for determining whether work is done during the gas's expansion.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In an insulated system, the internal energy change is equal to the heat added to the system minus the work done by the system. Since there is no heat exchange and no work done during the free expansion, the internal energy of the gas remains constant, which is essential for understanding the energy dynamics in this scenario.

관련 실천

교과서 질문

The air bags that provide protection in automobiles in the event of an accident expand because of a rapid chemical reaction. From the viewpoint of the chemical reactants as the system, what do you expect for the signs of q and w in this process?

885

views

교과서 질문

A sample of gas is contained in a cylinder-and-piston arrangement. There is an external pressure of 100 kPa. The gas undergoes the change in state shown in the drawing. (b) Now assume that the cylinder and piston are made up of a thermal conductor such as a metal. During the state change, the cylinder gets colder to the touch. What is the sign of q for the state change in this case? Describe the difference in the state of the system at the end of the process in the two cases. What can you say about the relative values of E?

564

views

교과서 질문

The automobile fuel called E85 consists of 85% ethanol and 15% gasoline. E85 can be used in the so-called flex-fuel vehicles (FFVs), which can use gasoline, ethanol, or a mix as fuels. Assume that gasoline consists of a mixture of octanes (different isomers of C₈H₁₈), that the average heat of combustion of C₈H₁₈(l) is 5400 kJ/mol, and that gasoline has an average density of 0.70 g/mL. The density of ethanol is 0.79 g/mL. (a) By using the information given as well as data in Appendix C, compare the energy produced by combustion of 1.0 L of gasoline and of 1.0 L of ethanol.

1969

views