2. Let A = A(T,V) and G = G(T,p) be thermodynamic state functions with total differentials dA = -SdT – pdV and dG = -SdT+V dp, where p, V, T, and S are, respectively, pressure, volume, temperature and entropy. a) Use dA and suitable relationships between partial derivatives to show that Cv dT + ()av dS (2) T av av as ƏT where a 1 1 and Cy = T K = V ƏT V

2. Let A = A(T,V) and G = G(T,p) be thermodynamic state functions with total differentials dA = -SdT – pdV and dG = -SdT+V dp, where p, V, T, and S are, respectively, pressure, volume, temperature and entropy. a) Use dA and suitable relationships between partial derivatives to show that Cv dT + ()av dS (2) T av av as ƏT where a 1 1 and Cy = T K = V ƏT V

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: (vii) Sketch the FD-distribution function at absolute zero temperature and at any finite non-zero…

Q: What are the following partial derivatives for the van der Waals gas? The number of moles, n, and…

A: Vanderwal equation for n mole gas : (P+n2av2)(v-nb) = nRT To find out :- (i) (OVOP))T (ii) (OVOT)P

Q: Question 2 The molar volume of a certain solid is 142.0 cm³ mol-¹ at 1.00 atm and 427.15 K, its…

Q: Much of the gas near the Sun is hydrogen nuclei. Its temperature would have to be 1.5 × 107 K for…

Q: question 4.4 from thermodynamics and statistical mechanics an integrated approach written by scott…

A: The expression for the probability is,

Q: 2.00 mol of helium and 1.00 mol of argon are separated by a very thin barrier. Initially the helium…

A: Given data, UHeinitial=7500 J nAr =2 nHe=1

Q: What is the difference in molar Gibbs energy, due to pressure, when a system moves from the ocean…

Q: do part D please

Q: 2. In the reaction between hydrogen gas and chlorine gas to give hydrogen chloride gas spontaneous,…

A: We have to Predict the spontaneity based on the calculated values of enthalpy change, standard…

Q: 2.A 1.60-mol sample of hydrogen gas is heated at constant pressure from 296 K to 410 K. (a)…

Q: The highest building in Montreal is the ‘1 square building’, with a height of 203m. The…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 4. Consider a diatomic molecule AB with masses mA =m, mg = 2m. Let the equilibrium distance between…

Q: You lower the temperature of a 2.5 mol sample of Ar gas by 2.3°C at constant volume. For monatomic…

Q: Calculate the absolute entropy of uranium (3.04 J/mol-K) at 20K. Show the complete solution please.…

Q: Suppose there are 10 distinguishable particles in a box divided into two equal compartments, A and…

A: The total number of distinguishable particle is N=10 The initial particles in the compartment A and…

Q: In interstellar space it is estimated that atomic hydrogen exists at a concentration of one particle…

Q: Suppose you have two meter sticks, one made of steel and one made of invar (an alloy of iron and…

A: Introduction: Thermal expansion is the tendency of the body to change its size and shape in the…

Q: This is a modified Stirling cycle. The Stirling engine never caught on due to industrial…

A: The given values are,

Q: H.W) Use the following data to calculate AG at 298 K for the combustion of propane: Substance…

A: The table given in the problem represents the different values of energy per mole of C3H8(g), O2(g),…

Q: 2- There is a system consisting of N independent particles. Each particle can have only one of the…

A: We have N independent particles existing in two energy levels Eo and -Eo. Let number of particles in…

Q: 19.42 · A thermodynamic sys- tem is taken from state a to state Figure P19.42 c in Fig. P19.42 along…

Q: 2 ЗР 3 P 1 4 V 4v V 33. An ideal gas is taken through a closed path 12-3→4-1. What is the net work…

A: Answer:- (A) 6 PV Given Change in pressure (∆P) = (3P - P) = 2P Change in volume (∆V) = (4V - V) =…

Q: Consider a star that is a sphere with a radius of 6.38 108 m and an average surface temperature of…

A: Given data: Radius R =6.38×108 m Star's temperature T= 5200 K Universe's temperature T'= 2.73 K

Q: 3) A human body has a temperature of 98.6 °F ( 37 °C or 310 K) on average, if the outside…

Q: 7. Now suppose that the box contains 1023 gas molecules. Use your formula to calculate the…

Q: 10.3. From the differential equation for the thermodynamic potential A(T, V), derive expressions for…

A: The solution is given below

Q: The equation of state for a certain gas under isothermal conditions is PV = 36 where the units are…

Q: Suppose you have two meter sticks, one made of steel and one made of invar (an alloy of iron and…

Q: 1- a) Consider a physical system composed of N identical particles confined to a space of volume V.…

Q: 1). If the Sun creates 3.85 X 1026 w of power at a temperature of 5800 K, what is the total entropy…

Q: 1. Which of the following thermal variables is not a state function? a. Pressure b. Internal Energy…

A: Correct answer is option (e) i.e. work

Q: In interstellar space it is estimated that atomic hydrogen exists at a concentration of one particle…

Q: A sample containing 1.00 kmol of helium (treated as an ideal gas) is put PA through the cycle of…

Q: H.W) Use the following data to calculate AG° at 298 K for the combustion of propane: Substance…

Q: One type of gas mixture used in anesthesiology is a 50%/50% mixture (by volume) of nitrous oxide…

A: Consider the gas’s initial temperature be T1, the gas’s initial pressure be P1, the gas’s final…

Q: Rather than insisting that all the molecules be in the left half of a container, suppose we only…

A: Introduction: Multiplicity of a mono atomic ideal gas is given by Ω(U,V,N)=f(N)VNU3N2 f(N)is a…

Q: A plastic bag containing 0.2 kg of water at 20°C is dropped from a height of 0.5 m onto an…

Q: Question 2 The internal energy of n moles of an ideal gas depends on A. one state variable T. B. two…

A: The internal energy of n moles of an ideal gas depends on

Q: *80. D The sun is a sphere with a radius of 6.96 X 10° m and an av- erage surface temperature of…

A: r=Radius of the Sun=6.96×108 mTs=Temperature of the Sun=5800 KTr=Temperature of the rest of the…

Q: One type of gas mixture used in anesthesiology is a 50% / 50% mixture (by volume) of nitrous oxide…

A: From Dolton’s law, total Pressure= Pn + Po; where Pn and Po are pressures from N2O and O2…

Q: dN F(V)dV = ‚MV² V² exp( 2RT M = 47(- , 2nRT AP(= where dN, the number of particles having a…

A: Given that,

Question

I need help with my problem. I do not know how to approach it. Show me detailed steps.

2. Let A = A(T,V) and G = G(T,p) be thermodynamic state functions with total
differentials dA = -SdT – pdV and dG = -SdT + V dp, where p, V, T, and S are,
respectively, pressure, volume, temperature and entropy.
a) Use dA and suitable relationships between partial derivatives to show that
Cv aT + ()av
dS
(2)
T
where a = +().,
÷(), and Cy = T()
1
1
K
ƏT
T
b) Use dG and suitable relationships between partial derivatives to show that
Cp
dT – aV dp
dS =
(3)
where C, = T().
as
ƏT
c) Use (2) and (3) and suitable relationships between partial derivatives to show that
Cp = Cy +TVª²
(4)
K
d) For a particular material, the values of Cp, a, and k as a function of tempera-
ture and pressure are readily available. A mole of this material is subjected to an
expansion process from V to V2 during which the temperature is observed to change
from T1 to T2 in a manner that depends with volume as T
constants to be determined). Use (2) and (4) to find an integral expression for the
change in entropy for this process, AS1→2 =
experimentally accessible quantities Cp, a, and K.
= a + bV (a and b are
S(T2, V2) – S(T1, Vị), in terms of the

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

Step 8

Trending now

This is a popular solution!

Step by step

Solved in 8 steps with 8 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

2. The following questions deal with the entropy of a system. Standard state is p = 1 bar and T 298K. a. Determine the standard molar entropy for N2O, a linear triatomic molecule where В — 0.419 ст-1, ў1 1285 ст-1, (doubly degenerate), and õz -1 = 589 cm 2224 ст.
Problem 1: In statistical mechanics, the internal energy of an ideal gas is given by: N. aNkB 2/3 (3NKB U = U(S,V) = е where a is a constant. 1- Show that the variation of the internal energy is given by: 2 dS - \3V 2 dU = dV \3NkB 2- Using the fundamental relation of thermodynamic dU = T.ds – p. dV, show that the equation of state PV = nRT follows from the first expression of U.
define the chemical potential in terms of derivatives of the ĈE energy E and enthalpy H. For a one component system, these are u= ON and Evaluate these expressions for an ideal gas and compare to ON µ = -kT In (kT/PA³ ) from H=| P,s OF and |= 1 TP ON v.r
An insulated box contains 10 gas molecules. Each molecule has the sameprobability of being in the left half of the box as in the right half. With n1molecules in one half of the box and n2 in the other determine i. All the possible configurationsii. No. of microstates for each configurationiii. Entropy of each configurationiv. Probability of each configuration.Write the results in the form of a table.
a) Find the difference of molar-specific heats Cp - C, for the gas covered by the equation of state: (P+) (V - b) = RT b) Determine the volume of the hypersphere in N-dimensional space. c) An ideal gas consists of N monatomic molecules. Using the grand canonical ensemble, (T-μ) distribution, calculate the chemical potential, pressure, and entropy.
1- a) Consider a physical system composed of N identical particles confined to a space of volume V. Write the thermodynamic limit for this system. b) Write condition of ideal gas for real gas. c) Prove B =, where The universal constant k is generally referred to as the Boltzmann constant. d) For a physical system composed of N identical particles at temperatureOand confined to a space of volume V, prove the ideal gas low PV = NkT
A bottle of volume V = 0.15 m³ contains helium gas (a monatomic gas) at a pressure p = 722,266 Pa (Pascal = N/m² and temperature T = 300 K. Calculate a numerical value for the internal energy U of this gas. Include units in your answer, using Sl units (m for meters, kg for kilograms, s for seconds, J for joules, K for kelvin, etc.). Write your answer as an exponential as described in the instructions.
Given the partition function of a certain gas is given by Z= C (V-nb)N (T3N/2), the entropy is given by O a. k (In C1 + In [T3/2/(V)]} O b. kN {In C1 + In (V-nb/ T3/2)} O C. kN (In C1 + In [(V-nb) T3/2]} O d. kN {In C1 + In [T3/2/(V-nb)]}
Problem 1: Gibbs free energy Derive the thermodynamic identity for G, where G = U + PV – TS, derive the three partial гaG derivative relations, S = - and u = P.N т.N
Ue A:0r * Il. pluls ► exam 1.pdf Q1// Define the following First law of thermodynamics, adiabatic process, Boyle's law, Reversibility, and Pressure. Q2// Ten kg of oxygen are heated from 350 to 500 K at constant pressure. Calculate the change of enthalpy, change internal energy, heat transfer and work done. Take Cp-0.909, Cv=0.649 Q3// In a nozzle air at 700°C and twice atmospheric pressure enters with 50 m/s velocity, and leaves at a temperature of 40°C. Determine velocity of air at exit. Take Cp = 1.005 kJ/kg.K for air.
Calculate the number of microstates that are available in a single atom of carbon in graphite.The standard molar entropy (S°) of carbon is 5.7 J/(mol · K) and the Boltzmann constant (kB) is1.381 × 10 ―23?/?. HELP PLEASE
Given the ideal gas law P V = k T, where k> 0 is a constant. We have the equation for V in terms of P and T. Finding the rate of change of the volume with respect to temperature at constant pressure, the interpretation of the result is: 1 Because this partial derivative is negative, the volume decreases as the temperature decreases at a fixed pressure. . 2. Because this partial derivative is negative, the volume increases as the temperature increases at a fixed pressure. 3. Because this partial derivative is positive, the volume increases as the temperature decreases at a fixed pressure. 4. Because this partial derivative is positive, the volume increases as the temperature increases at a fixed pressure.