10.2. Show that, for an ideal gas: (a) A = [Cydr - dT dT-nRTln V-const. T+ const. TSC / AT 1 (b) G= SCp dT - TSar dT+nRTln P-const. T+ const. (c) Apply the above equations to 1 mol of an ideal gas.
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- (1) The relationship between C P.m and C V.m can also be given by the relationship: CP.m - Cym = T| aT (a) Use the above equation to demonstrate that C P.m - C V.m - R for an ideal gas. (b) Demonstrate the expression C P.m - C V.m for a gas obeying the equation of state: PVm = RT + B(T)P(6) Consider an ideal gas for which pV = n RT. Determine the change in pressure, p, for n = 2.0 moles of an ideal gas when the temperature, T, is changed from 190K to 200K and the volume, V, is changed from 20L to 19L. The gas constant is R = 8.314 J• mol-1 • K-1. Express your answer in atmospheres. HINT: Use an expression for the total differential dp(T, V). Evaluate your partial derivatives at the point (V,, T¡) with the increments in volume dV = (V, – V,) and dT = (T, – T,)Study questions -chapt 18 1. Which of the following changes lead to a decrease in entropy? a. sugar dissolving in coffee b. mixing of pure gases c. the sublimation (vaporization) of dry ice (solid carbon dioxide) d. melting snow e. halving the volume of a gas 2 At what temperatures will a reaction be spontaneous if A,H° = +117 kJ and A,S° =-35 J/K? 3. Calculate A,G° for the following reaction at 425 °C, (8)I + (3)*H_, (3)IH given K= 0.018. (R=8.314 J/K-mol) %3D 4. For a reaction, A,H° = -208.8 kJ and A,S° =-308.2 J/K. At what temperature will A,G° = 0.00 kJ? %3D %3D 5. What is the sign of AH (system) and AS (system) if a chemical reaction is spontaneous at all temperatures under standard conditions? HV ε (system) is negative, and AS (system) is positive. HV °q (system) is negative, and AS (system) is negative. HV (system) is positive, and AS (system) is positive. HV P (system) is positive, and AS (system) is negative. e. none of these 6. For which of the following reactions will the…
- Substitute the equation from Step 2 into the given equation for P and complete the partial derivative. (Use the following as necessary: kg, Q, T, U, and Up.) P = - -(3+), T - (ain(@)), КВТ = KBT Step 4 of 7 For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.) (3V)₁ = 1 UT 0 Step 5 of 7 Give the equation for the canonical partition function Q. Remember that only the translational partition function needs to be considered for an ideal monatomic gas. (Use the following as necessary: e, h, kg, m, N, T, T, and V.) N (2πmkBT) Ve Nh³ Q = (2µmkµT)h³v X Step 6 of 7 Determine In(Q) using the equation for Q from Step 5. (Use the following as necessary: e, h, kB, M, N, π, T, and V.) Ve In(Q) N In (2μmkBT) Nh³ (2π m kBT) e N ln (V) + Nln Nh³ Substitute into the equation for P from Step 3 and solve the partial derivative. (Use the following as necessary: e, h, kg, m, N, π, T, and V.) NKB T P = V |KBTN- V Step 7 of 7 Rearrange the equation for P from Step…1.29. Determine the expressions for the following, assuming that the ideal gas law holds. av (2) (ap) ₁ (а) (Ь) (ы)(2) ( ), (c) ат av др (d) an T.p дл aT/va1) Show that for ideal gas: [dH= Cp dT] and dS= Cp dT/T-R dP 1 Add file
- 7. For an Ideal Gas, find the Partial Derivative of v, w.r.t. P. 8. Please consider large room that needs a new carpet. The vendor came and estimated the cost at $8 to $12 per square foot, depending on the condition of the sub-floor. The vendor then "paced off" the room and estimated that the room was 60° by 50’. You estimated that the vendor's method of measuring the room dimensions could be off by as much as 3' in for each dimension. Please find the (a) mean cost, (b) best case cost, (c) worst case cost, and (d) the most probable cost,6) Calculate the final temperature of a sample of carbon dioxide of mass 16.0 g that is expanded reversibly and adiabatically from 500 cm³ at 298.15 K to 2.00 dm³.Calculate TT for a gas that obeys the virial equation of state p = RT Vm B(T) (1+ + ...) Vm
- H5-1. 80 g of ideal Argon gas (Ar) are at a 1000 L cylinder and constant temperature of 300 K. The system is closed by a free moving, frictionless piston, and above it there is a weight with mass M applying pressure as shown in the figure. At a certain moment a second weight is added above with identical mass M and the system is compressed until new equilibrium is reached. M W, Pin Vin T = const M M W M M Pin Vin P₁ V₁ T = const T = const a. Calculate the work and the change in the internal energy of the Argon gas as a result of the compression process, given Q = - 4.99 kJ, Mw(Ar)= 40 g.mol-1. b. One weight is removed and the system returns to the original state, as described in the figure. Calculate the for the entire process the work and change in internal energy.ƏP ƏT V T 1. Calculus review. Derive expressions for the partial derivatives following equations of state for real gases. The parameters a and b are constants. The Dieterici equation (recall exp (x) is the same thing as e): nRT V - nb P = exp [- and na RTV. for theGiven these relation, prove this without usin Maxwell relatios as - ( ), aV ӘT JP/T P