Derive the following thermodynamic equation of state.ne= -P + TavApply the equation to the following.(a) an ideal gas(b) a van der Waals gasComment on your results.Step 1 of 7Derive the following thermodynamic equation of state.(),au= -P + TITavaTVDifferentiate the equation dU = –PdV + TdS with respect to V while keeping T constant to obtain an()asexpression forUse the following as necessary: P, S, T, V, and ASV¡ to representav ITavaunRTavV-P+T·ASVTStep 2 of 7(), and (), (uxIdentify the relationship betweenUse the following as necessary: P, S, T, V, and APTVto representas

Thermodynamic Equation of State. It is a thermodynamic equation relating state variables, which…

Answered: Derive the following thermodynamic…

Derive the following thermodynamic equation of state. %3D = -P + av. Apply the equation to the following. (a) an ideal gas (b) a van der Waals gas Comment on your results.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

See similar textbooks

Related questions

Q: 1. Calculus review. Derive expressions for the partial derivatives (3) T and following equations of…

Q: 3.63 moles of a gas that follows the van der Waals equation of state are placed in a rigid container…

Q: The relationship Cp - Cy = a?TV holds for any substance in the gaseous, liquid, or solid state. = ,…

Q: 1.29. Determine the expressions for the following, assuming that the ideal gas law holds. av (2)…

Q: 3 2.25 moles of an ideal gas with C, m =-R under a constant external pressure of 200.0x10³ 2 3. Pa…

Q: Answer all questi 1) One mole of an ideal monoatomic gas initially at 55°C is expanded reversibly…

A: The objective of the queston is to calculate-

Q: The equation of state of a liquid gives the volume as a function of the temperature and pressure: V…

Q: 1. (Hw) A cylinder with a piston contains 0.25 mol of nitrogen at 1.80 x 10'Pa and 300 K. The…

A: The gas is first compressed isothermally one-half of its original volume. It then expands…

Q: | 2.25 moles of an ideal gas with C, m 3 =-R under a constant external pressure of 200.0x10 2 3. Pa…

A: Given data

Q: (a) Determine the units of the constants (b) Develop an equation to calculate Cp in (Jxgmol-1xK-1)…

Q: Starting with the following alternative definition of Cp, and C₁: C = (S/S), C₁ = T(ƏS/ƏT)v show…

A: The problem asks us to show that Cp − Cv can be expressed as a function of PVT properties only,…

Q: Calculate the final temperature and the change in enthalpy when 765 J of energy is transferred as…

A: The solution is given below:

Q: An automobile wheel contains air with a pressure of 3x105 Pa at 25 ° C. The sipop cover was removed…

Q: - Evaluate for an ideal gas and a van der Waals gas. Hint: [CY] = T(07²),

Q: = 4. Assume N2 behaves as perfect gas. A sample consisting of 2.00 mole of N₂ initially at pi 111…

Q: Calculate TT for a gas that obeys the virial equation of state p RT Vm B(T) Vm = (1+ ·+ ...)

Q: + e H2O a) Write the equations for the balance by elements and the balance of electrons. b)…

A: Part a. and b. amount of carbon in 1 mole of substrate = 2(12) = 24 g amount of carbon converted to…

Q: An automobile wheel contains air with a pressure of 3x10^5 Pa at 25 ° C. The sipop cover was removed…

A: The relation between pressure and temperature for the adiabatic process is shown below: where; P =…

Q: Gas Constant R of CO2 at 825K.

A: Gas constant is a universal constant and its value is fixed for all gases. It does not change with…

Q: If 293 J of heat is required to raise the temperature of 2 mol of an ideal gas at constant pressure…

Q: Five moles of monatomic ideal gas enter the abc cycle and during a complete cycle 600 J of heat is…

A: As 600J heat is removed from the process. Thus abc cycle is transferred from higher temperature to…

Q: Die standaard verbrandingsentalpie van sikloheksaan (C6H12,1) is -3920 kJ.mol1 by 25 °C. Gebruik…

Q: Metabolic engineering Consider the engineering design of microbial cell culture and growth in the…

A: Given:Reaction is: C2H5OH + aO2 + bNH3 -----> cCH3.5N0.15O0.4 + dH2O + eCO2 By mass…

Q: A mixture of 1 kmol of gaseous methane and 2 kmol of oxygen initially at 258C and 1 atm burns…

A: To solve this problem, we need to calculate the amount of heat transfer during the combustion…

Q: 圖) V- b SP (2a/RV³)(V – b)? –T

A: A van der Waal gas or a real gas is a gas that follows the van del Waal equation which will be as…

Q: The

Q: A sealed, insulated container is divided into 2 sections by a very thin membrane. Section A contains…

Q: Molecular weight of a certain volatile liquid which is placed in 225 g flask which has total…

A: According to the question, we need to determine the molecular weight of the volatile sample. Given:…

Q: (i) A thermally insulating container has a membrane separating the container into two equal parts.…

A: The statement which is not true for the gas is: D) There is no entropy change for the system.

Q: • As T& C.p's speed change, IeFs stay "on" in ~ the same % level, then step ↑ or Į to a different…

A: The phase of the substance is associated with how closely the molecules or the atoms of the…

Q: (c) The Cp of a sample of a perfect gas is related to the temperature as shown below: Cp/(J.K-1) =…

A: I Hope this helps you 🙏.Please give Student Rating ----> If you Found it Helpful. ( I really…

Q: An automobile wheel contains air with a pressure of 3x105 Pa at 25 ° C. The sipop cover was removed…

A: Adiabatic expansion process occurs without transfer of mass or heat between the system and it's…

Q: At 298 K. AH;131.28 kJ-mol for the reaction with Op.-8.53, 33.58, 29.12, and 28.82 J-K-mol for…

A: Given data :

Q: 1 mol of an ideal gas at 25 ° C and 10 atmospheres (Cp = 3.5 R), adiabatically and reversibly 5 What…

A: Welcome to bartleby !

Q: Calculateur (298.15 K, 1 bar) for nitrogen in air, assuming that the mole fraction of N₂ in air is…

Q: E2A.5(b) A sample consisting of 2.00 mol of perfect gas molecules, for which Cy.m = ³R, initially at…

Q: 3. Using the definition of isothermal compressibility (k): 1 -= (-). ӘР T Solve for K for an ideal…

Concept explainers

Kinetic-Theory of Gases

Kinetic theory of gases is the model or method which was developed in the 19th century by Maxwell and Boltzmann. This is possible as the interatomic force which is of short-range forces that are important for solids and liquids can be neglected for gases. This theory or gas law gives a molecular interpretation of the pressure and temperature of a gas and is consistent with gas laws and Avogadro’s hypothesis. This theory is very helpful to correctly explain the specific heat capacities of many gases, kinetic energy and it also explains the transport qualities such as viscosity, thermal conductivity, and diffusion with molecular parameters. As stated in the kinetic-molecular theory, the temperature of a substance or gas particle is related to the average kinetic energy of the particles of that substance. When a substance is heated, some of the absorbed energy is stored within the particles, while some of the energy increases the motion of the particles, called average kinetic energy.

Question

Derive the following thermodynamic equation of state.
ne
= -P + T
av
Apply the equation to the following.
(a) an ideal gas
(b) a van der Waals gas
Comment on your results.
Step 1 of 7
Derive the following thermodynamic equation of state.
(),
au
= -P + T
IT
av
aT
V
Differentiate the equation dU = –PdV + TdS with respect to V while keeping T constant to obtain an
()
as
expression for
Use the following as necessary: P, S, T, V, and ASV¡ to represent
av IT
av
au
nRT
av
V
-P+T·ASVT
Step 2 of 7
(), and (), (ux
Identify the relationship between
Use the following as necessary: P, S, T, V, and APTV
to represent
as

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

For the gas reaction CO (g) + O₂ (g) → CO₂ (g) Calculate the maximum volume of the CO₂ gas at 28 C° and 100 Kpa, which can be produce from reacting 500 cm³ of CO gas at 105 Kpa and 15 Cº with 500 cm³ of oxygen gas at 110 Kpa and 0 Cº.
2. A system consists of 1 mole of ideal gas is taken through the cycle shown below from (1→2 →3). For this ideal gas, Cp = 5R/2 and C+ = 3R/2 (a) Determine the temperature (in units of K to 4 sig. figs) at the points, 1, 2, and 3 For (b), (c), and (d) please report q, w, AU, and AH in units of kJ to 3 sig. figs. If an answer is 0, then just put 0 for the answer. (b) Calculate q, w, AU, and AH for step 1-2 (in other words as the system is taken from an initial state at point 1 to a final state at point 2) (c) Calculate q, w, AU, and AH for step 2→3 (d) Calculate q, w, AU, and AH for step 3→1 1.0 P (atm) 0.5 1 22.4 isotherm V (dm³) 44.8
Please don't provide handwritten solution ....
Hello, I understand that cp for diatomic ideal gas is 7/2R. How do I find the same for a gas like carbon dioxide?
A7. (a) Given that for an ideal gas (0) AG=nRT In aG ap =V, show that for a change in pressure from P₁ to P₂ ompression of two
2. For the volumetric properties of pure fluids, two parameters are the volumetric expansivity and the isothermal compressibility, whose formula are given below: 1 av от 1 Ov K=-- Using these parameters, derive a formula for volume as a function of temperature and pressure
A certain gas obey's the following equation of state: RT P = V – b V²T a Write the constants a andb in terms of the critical P V. and T?
4. The equation of state for a van der Waal's gas is: RT V-by², where Vm is the molar volume, V/n. p= m a m Starting with an expression for U(S,Vm), derive an expression for the internal pressure, TT, and calculate its change when a van der Waal's gas with a = 4.14 atm L²mol-2 and b = 5.15 x 10-2 Lmol-¹ is cooled from 200°C to 10°C.
Xenon and helium are both ideal, monatomic gases, but they have very different molar masses (Mxenon = 33*Mhelium). If you have 1 mole of each gas and the gases are at the same temperature, which one of the following statements is true? They both have the same internal energy, but xenon has a lower root-mean-square speed than helium. They both have the same internal energy and root-mean-square speed. They both have the same root-mean-square speed, but xenon has a greater internal energy than helium. They both have the same internal energy, but helium has a lower root-mean-square speed than xenon. They both have the same root-mean-square speed, but helium has a greater internal energy than xenon.
Two ideal gases, one monoatomic and the other diatomic are mixed with one another and form an ideal gas again. The equation of the adiabatic process of the mixture is 11 PVY= = constant; where What is the ratio of the number of molecules of the monoatomic gas to that of the diatomic gas in the mixture?