Show that the statistical definition of the internal energy (U = E, E,p;) and the entropy (S = -k E;p; In(e;)), where (p;) is the Boltzmann distribution, are consistent with the differential form of the fundamental equation of thermodynamics (dU = T'dS - PdV).
Q: 2. 2 dm of methane under 4 bar and 298 K and 4 dm³ of oxygen under 2 bar and 298 K. are forced into…
A:
Q: True or false For a closed system at rest, the sum q + w has the same value for every process that…
A:
Q: Calculate the change in the entropies of the system and the surroundings, and the total change in…
A: Part a- Since the total entropy is zero for isothermal reversible expansion, the entropy of the…
Q: se dp +| dS = se dT Use (ƏS/ƏT), = C,/T and an appropriate Maxwell relation to show that TdS = C,dT-…
A: SOLUTION: Step 1:
Q: Given that the Gibbs energy is a function of temperature and pressure G(T, P), estimate the change…
A: Gibbs free energy is a thermodynamic parameter which helps us in finding the maximum work done by a…
Q: One mole of a monatomic ideal gas begins in a state with P 5 1.00 atm and T 5 300 K. It is…
A: There are two ways to solve this answer. Easy Way- Entropy is a sate function. Its value depends on…
Q: Derivation Starting with the relation P = -(JA/V)T, show that P = kBT(à In Q/V)T. Using argon as an…
A:
Q: Thermophysical properties of 1,1,1,2-tetrafluoroethane (refrigerant HFC-134a) has been published (R.…
A:
Q: A sample of blood plasma occupies 0.550 dm3 at 0 °c and 1.03 bar, and is compressed isothermally by…
A: GIVEN: Initial volume of the sample of blood plasma Vi=0.550 dm3 at 0 °c Pressure=1.03 bar. constant…
Q: dU = Cv dT + PT dV where Cv is the constant volume heat capacity and PT is the internal pressure.…
A: In thermodynamics, various functions are involved. They are derived from other functions using…
Q: The molar heat capacity of oxygen at constant pressure can be expressed as follows: Cp,m = a + bT,…
A: Given data, Moles of oxygen = 2 moles Initial temperature(T1)=27oC Final temperature(T2)=127oC…
Q: Given a thermodynamic function h=h(s,p) show how to evaluate T, V , U , A or F and G
A: Given function, h=h(S,P)By ditferenciating we get,dh=∂h∂SPds+∂h∂pSdp — (I)From Gibbs realtion, dh…
Q: Consider this modified equation of state: nRT P: V-nb as a. Evaluate the term (85) for the equation.…
A: We have a modified equation of state which is given by P=nRTV-nb If we expand this equation, we will…
Q: 4. Calculate the AS (system) for the reversible heating of 1.0 mol of ethane from 300 K to 1800 K at…
A: entropy is a thermodynamic property Here we are required to find the entropy of the system for…
Q: Calculate ΔrH⦵ and ΔrU⦵ at 298 K and ΔrH⦵ at 427 K for the hydrogenation of ethyne (acetylene) to…
A: As table is not given here, so taking standard values form Google. The heat of combustion of ethyne…
Q: Can the variation of specific heat Cp with pressure at a given temperature be determined from a…
A: It depends on whether we are consider For real gas or ideal gas [XP/OP]T = d/dP [(dH/dT)P]T
Q: 5.Derive Entropy of mixing for an ideal solution derive ASmix= -k(N,LnX,+N„LnXs) using i. Classical…
A: Entropy of mixing, in thermodynamics, is the increase in the total entropy when several initially…
Q: In constant temperature, closed system process, 120 BTU of heat is a transferred to the working…
A:
Q: Two moles of a perfect gas expand isothermally and reversibly from 800 cm3 to 300 dm3 at 310 K. (a)…
A: Work done in a reversible isothermal process is the increase in volume at constant temperature and…
Q: A sample of 70. mmol of Kr (g) expands reversibly and isothermally at 373 K from 5.25 cm3 to 6.29…
A:
Q: Compute for Delta U, Delta H and W if 5 moles of an ideal diatomic gas undergoes an isochoric…
A: Answer: In isochoric process volume of system remains constant all throughout the process.
Q: The standard molar entropy of N2 gas at 25 ⁰C can be determined experimentally from S(0) through…
A: Solution - According to the question - Given values are - For N2(s) ----> N2(l) ; ∆sm =…
Q: 78.1 g of C6 H,OH(s) at 300. K are transformed to C6 H,OH(1) at 320. K with an increase in entropy…
A: The enthalpy of fusion is the energy required for changing a substance from its solid state to its…
Q: Helium is compressed isothermally and reversibly at 100 °C from a pressure of 2 to 10 bar. Calculate…
A:
Q: A sample consisting of 0.5 mol of perfect gas molecules with CP,m = 20.8 J · K. mol is initially at…
A:
Q: calculate the final temperature of a sample of carbon dioxide of mass 16.0g that is expanded…
A:
Q: Liquid ethanol C,H;OH at 25 °C, 1 atm enters a combustion chamber operating at steady state and…
A:
Q: Calculate the entropy of HBr at 298 K and 1.00 bar, given that the bond length is 1.41 Å and the…
A:
Q: The differential for the Gibbs function, G, at constant composition is: dG = −S?T + Vdp write the…
A:
Q: A. Consider the following gas phase reaction: H20 (g) → H2(g) +02(g). Using the tabulated…
A:
Q: A sample consisting of 2.00 mol of perfect gas molecules, for which Cy =R, initially at pi = 170 kPa…
A: 2.0 mole of a perfect gas having initial pressure at 170 kPa and T1 = 277 K is heated…
Q: V. P. Kolesov et al. (J. Chem Thermodynamics 28 (1996) 1121) reported the standard thalpy of…
A: standard specific internal energy = -36.0334 kJ/g Molar mass os C60 = 720.6 g/mol The combustion…
Q: P =126 kPa and T1= 300 K, is heated reversibly to 500 K at constant volume. Calculate w, q, Δυ ΔΗ
A:
Q: xygen is compressed polytropically in a cylinder from 1.5 bar, 15oC to 4.2bar in such a way that 1/3…
A: According to the first law of thermodynamics energy is always conserved. This energy is converted…
Q: When 3.0 mol O2 is heated at a constant pressure of 3.25 atm, itstemperature increases from 260 K to…
A: Thermodynamic quantities depend upon Temperature, pressure and volume. Enthalpy, internal energy and…
Q: For ethanol, ΔvapH⦵ = 43.5 kJ mol−1. Calculate q, w, ΔH, and ΔU when 1.75 mol C2H5OH(l) is vaporized…
A: Enthalpy is a thermodynamic quantity that can be calculated by adding the internal energy of a…
Q: The molar heat capacity of N2(g) in the range 200K to 400K is given by Cpm (J/Kmol)=…
A: Given: Standard molar entropy of N2(g) at 298K (ΔS1) = 191.6 J/Kmol Initial temperature = 25 oC =…
Q: Calculate the entropy of HBr at 298 K and 1.00 bar, given that the bond length is 1.41 Å and the…
A: Srot=R ln 8π2IkBTσh2+R (1)
Q: 2. Two vessels of equal volume are perfectly insulated and contain the gases at the temperatures…
A:
Q: (b) For any thermodynamic equation of state: (ƏH (F), = V -T P an² Derive an expression for () for…
A:
Q: (b) For any thermodynamic equation of state: ), =v - r ), ӘР. ле an Derive an expression for a (O,…
A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: 2. A7.0 x 102 mol sample of Kr (g) expands reversibly and isothermally at 373 K from 5.25 mL to 6.29…
A: Bkr=-28.7mL/molBy virial equationP=RTVm(1+BKrVm)Expression for work doneW=-∫ViVfp.dVPutting the…
Q: molar heat capacity of white tin (Sn( white)) varies with temperature as follows:
A: Given that,
Q: From the data in Table 2C.4 of the Resource section, calculate ΔrH⦵ and ΔrU⦵ at (i) 298 K, (ii) 478…
A: The given temperatures are i) 298K ii) 478K The given reaction is C(graphile) + H2O(g)→CO(g)+…
Step by step
Solved in 2 steps with 2 images
- Without carrying out an explicit calculation, explain there lative values of the standard molar entropies (at 298 K) of the following substances: (a) Ne(g) (146 J K-1 mol-1) compared with Xe(g) (170 J K-1 mol-1), (b) H2O(g) (189 J K-1 mol-1) compared with D2O(g) (198 J K-1 mol-1), (c) C(diamond) (2.4 J K-1 mol-1) compared with C(g raphite) (5.7 J K-1 mol-1).Half a mole of a perfect gas expands isothermally and at 298.15 K from a volume of 10 L to avolume of 20 L. (a) What is the change in the entropy of the gas? (b) How much work is doneon the gas? (c) What is the heat of Surroundings ? (d) What is the change in the entropy of the surroundings? (e)What is the change in the entropy of the system plus the surroundings?The temperature dependence of the heat capacity of non-metallic solids is found to follow the Debye T3 -law at very low temperatures, with Cp,m = aT3. (a) Derive an expression for the change in molar entropy on heating for such a solid. (b) For solid nitrogen, a= 6.15 x 10-3 J K-4 mol-1. What is the molar entropy of solid nitrogen at 5 K?
- se dp +| dS = se dT Use (ƏS/ƏT), = C,/T and an appropriate Maxwell relation to show that TdS = C,dT- aTVdp, where the expansion coefficient, a, is defined as a= (1/V)(av/ƏT),. Hence, show that the energy transferred as heat, q, when the pressure on an incompressible liquid or solid is increased by Ap in a reversible isothermal process is given by q = -aTVAp. Evaluate q when the pressure acting on 100 cm' of mercury at 0°C is increased by 1.0 kbar. (a= 1.82 × 10*K'.) P3E.6 Suppose that S is regarded as a function of p and T so thatGiven that the molar entropy of a gas is: (+) SN=Na = R + Rln SN=Na = R + Rln ((² *² + RT i) Show that the molar entropy of a monatomic ideal gas (ignore electronic energy for now) can be written as (P is pressure): 12 * π *m* h² d(ln(q))) dT * T KB 3/2 * R* T V Navog * P 3 +-R ii) Calculate the molar entropy of Xe(g) at 298.15 K and compare this to the literature value. iii) Show that the change in entropy due to expansion for an ideal, monatomic gas is the same when using either a partition function approach or a thermodynamic approach.The constant pressure heat capacity of a perfect gas was found to vary with temperature according tothe expression ??( ? ?−1) = 20.17 + 0.4001 ? (?). Calculate q, w, change of U, and change of H when the temperatureis raised from 25 C to 100 C (i) at constant pressure, and (ii) at constant volume.
- (a) Which of the thermodynamic quantities T, E, q, w, andS are state functions? (b) Which depend on the path takenfrom one state to another? (c) How many reversible pathsare there between two states of a system? (d) For a reversibleisothermal process, write an expression for ΔE in terms of qand w and an expression for ΔS in terms of q and T.Derivation Calculate the entropy of HBr at 298 K and 1.00 bar, given that the bond length is 1.41 Å and the masses of ¹H and 79Br are 1.008 amu and 78.92 amu, respectively. The vibrational wavenumber is 2649 cm-1. Step 1 of 7 Provide the equation needed to calculate the translational contribution to the total entropy. (Use the following as necessary: h, kB, m to represent the mass, P, π, and T.) (31) BT) = R In Strans (2μmk B¹ h³ KBT (2πmkBT) kBT P h³ P Step 2 of 7 Substitute numerical values into the equation from Step 1 to obtain a numerical calculation for the translational entropy contribution. XJ.K-1.mol-1 Strans =146.211 SubmitDerivation Calculate the entropy of HBr at 298 K and 1.00 bar, given that the bond length is 1.41 Å and the masses of ¹H and 79Br are 1.008 amu and 78.92 amu, respectively. The vibrational wavenumber is 2649 cm-¹. Step 1 of 7 Provide the equation needed to calculate the translational contribution to the total entropy. (Use the following as necessary: h, kB, m to represent the mass, P, T, and T.) (²³1) (2πmkT) h³ Strans = R In kµT (²/2) e P (2πmkBT) ³ kBT h³ P Step 2 of 7 Substitute numerical values into the equation from Step 1 to obtain a numerical calculation for the translational entropy contribution. Strans = 163.61 163.484901080763 J.K-1.mol-1 Step 3 of 7 Provide the equation needed to calculate the rotational contribution to the total entropy. (Use the following as necessary: h, I, kB, 7, σ, and T.) Srot = R In 8n²lkpT oh² + R 87² IkBT oh² Step 4 of 7 Substitute numerical values into the equation from Step 3 to obtain a numerical calculation for the rotational entropy…
- 7:53 PM Mon Nov 21 < TOA 5.) A sample of 2.00 mol of a perfect gas is initially at a pressure of 111 kPa and temperature of 277 K. The sample is heated reversibly to 356 K at a constant volume. The constant volume molar heat capacity is 2.5R. Calculate the final pressure, AU, q, and w. n= 2.00 mol AT= 356 K-277 K= 79 K P= 111 kPa 1.11x 10³ Pa Cp.m= 2.5R = 2.5.8.314 / mcl.k= 20.79 J/mol K F w=0 AU= q Reversible pressure inside is same as pressure outside = m CSAT @87% q= 4 8Calculate the energy transferred as work, Wsys, for; (a) a gas that is compressed irreversible from 500 cm3 to 150 cm3 by an external pressure of 20 kPa; (b) 2.2 moles of a gas that is compressed reversibly at 120C from an initial pressure of 2.4 to a final pressure of 1.1 Torr.Whenever a gas expands when we exhale, when a flask is opened, and so on the gas undergoes an increase in entropy. Conversely, when a gas contracts, its entropy decreases. (a) Show that the entropy change đue to reversible isothermal expansion or contraction of a perfect gas is AS = nR In(V¼V;), where V; and V; are the initial and final volumes, respectively. (b) Calculate the change in molar entropy when carbon dioxide expands isothermally from 1.5 L to 4.5 L. (c) A sample of carbon dioxide that initially occupies 15.0 L at 250 K and 1.00 atm is compressed isothermally. Into what volume must the gas be compressed to reduce its entropy by 10.0 JK-