Question

Asked Jun 11, 2019

This problem is (6.10) from a book "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"

Step 1

Part (a): Given that the container is well insulated, *N* moles of a monoatomic ideal gas expands irreversibly from initial volume *V _{1} = V* to final volume

As the given system is thermally well insulated, there will be no exchange of heat between system and surrounding. Also, no work is done on the surrounding as gas is freely expanding against vacuum. Now, according to first law of thermodynamics expressed by equation (1), since work done and heat exchange is zero, as a result change in internal energy *ΔE* is also zero.

For an ideal gas, change in internal energy is the function of temperature only. Therefore, the temperature of the system remains constant, making the process isothermal.

For an isothermal process involving ideal gas Boyle’s law is applicable which is represented in equation (2). Since, volume is doubled therefore, the pressure will be halved according to equation (2).

Step 2

It is known that the entropy is a state function, meaning, it depends on final and initial state of the system, rather than the path followed by it. Let us assume a reversible path that brings about the given change in volume. Entropy of the surrounding will be zero, as there is no interaction of system with the surrounding. Entropy of the system for the defined path is then given by equation (3).

Part (b): The relation for entropy represented in equation (4) is applicable for reversible processes only. Here, the free expansion of an ideal gas is an irreversible process. Therefore, entropy change do not correspond to the heat transfer in this case.

Step 3

Part (c): As the gas is expanding reversibly now in a well-insulated container, proceed by considering the process to be adiabatic. An adiabatic process follows equation (5) where k is constant....

Tagged in

Q: .19 A liquid storage facility can be modeled by where y is the liquid level (m) and u is an inlet fl...

A: Part (a):Since all the derivatives are zero and y=u=0 at the nominal steady state, hence taking Lapl...

Q: Please answer part (g) only.

A: Part g:The part can be solved in two ways:Apply final value theorem and find the ultimate value of t...

Q: The standard heat of reaction for the production of formaldehyde in the reaction, 2 CH3OH (l) + O2 (...

A: Click to see the answer

Q: Ethylene oxide is formed by the partial oxidation of ethylene. Unfortunately some of the ethylene is...

A: Part (a) The schematic diagram of the given process is shown below.

Q: A bottle of carbonated water contains a liquid and vapor in equilibrium. The liquid contains 0.01mol...

A: Let the ideal mixing of components in liquid and vapor phases, Raoult’s Law is used for the given qu...

Q: Homework #1 1.18 Nitrogen gas can be injected into oil wells to increase the recovery of crude oil (...

A: Part (a)Note: As the table 1.2 and 1.3 was not provided with the question so, conventional symbols a...

Q: Chemical and Bio-Process Control 4edSensor Systems:Consider flow sensor that reads 10,000 lb/h when...

A: Zero is the lowest value of the range in the measuring instrument and span is the difference between...

Q: For a test of enzyme-catalyzed kinetics, the following data were recorded product (mmol/mL) (mmol/mL...

A: Part (a)Michaelis-Menten equation to be used is written as equation (1).The reciprocal equation of (...

Q: H3CA is a vitally important intermediate in the metabolism of carbohydrates. The compound is widely...

A: Part (a):It is given that 21.35 mL of 0.678 M NaOH(aq) requires to fully neutralize 0.927 g of H3CAA...