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Please i need Mathematical proof this equation
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- Define isobaric,isochoric, isenthalpic,and isothermal. Can achangein a gaseous system be isobaric, isochoric,and isothermal at the same time? Why or why not?Show that = T/p for an ideal gas.What is the finaltemperature of0.122 mole ofmonatomic ideal gas that performs 75J of work adiabatically if the initial temperature is 235C?
- (7) Combustion of CH4 and H₂. For 100 g mol of a gas mixture of 75 mol % CH4 and 25 mol % H₂, calculate the total heat of combustion of the mixture at 298 K and 101.32 kPa, assuming that combustion is complete.The Gibbs Function G is a thermodynamic property. If following relationship as Ꮩ . (ap)T = -(T)P p=-S and = V, prove the7:53 PM Mon Nov 21 8) A sample of 1 mol of perfect gas at 298 K and 1 bar with Cvm = 3/2 R and Cp.m= 5/2 R is put through the following cycle: (a) constant-volume heating to twice its initial pressure, (b) reversible, adiabatic expansion back to its initial temperature, (c) reversible, isothermal compression back to 1 bar. Calculate q, w, AU, and AH for each step, as well as any necessary variables (e.g. V₁, T, etc.) n=1 mol T= 298 K P= I bar Cum 3R - 2 Cp.m-2R T b) a) w=0 n=1 T= 298 K Cvm = 3R 2 AP= 1 bar 9,² AU= ΔΗ: PV = nRT V = nRT @87% 8
- 2.0 atm adiabatic isothermal 16.0 L 40.0L V A thermodynamic cycle of 1.000 mol of monoatomic perfect gas (Cv,m = 12.47 JK1 mol1) consist of the following 3 stages: STAGE 1:1 to Il ; adiabatic reversible expansion from(T1 =273K, V:= 16.0 L, P1= 2.00 atm) to (T2= ?, P2=1atm, V2= 40.0 L) STAGE 2, Il to Il ;isothermal reversible compression from (T2 =?, V2 = 40L, P2 = 1.00 atm) to (T3 = ?, V3 = 16L, P3=?) STAGE 3: IIII to l; isochoric heating from (T3 =?, V3 = 16 L, P3 = ?) to (T1 = 273K, V = 16 L, P1 = 2 atm) What is the Stage 1 final temperature, T,? Answer in Kelvin in 3 significant figures. Type your answer. What is the change in internal energy (in kJ) in the Stage 1 process? Answer in 3 significant figures. Type your answer. 2 points Calculate q (in kJ) for the Stage 2 process. Answer in 3 significant figures. Type your answer. point Calculate q (in kJ) for the stage 3 process. Answer in 3 significat figures Type your answer. What is the overall change in internal energy (in kJ) for…12. Consider 0.1 mole of a monotomic ideal gas (system) which is initially equilibrated at a tem- perature of 500 K in a container with a volume 1 of 1 m³, and then undergoes a reversible norisothermal expansion to a volume of 2 m³. 200(a) What is the energy change of the gas (in J units)? Seemee axismo (b) How much work is exchanged in the above process (in J units)? emoldong slon Su for (c) What is the entropy change of the gas (in J/K units)? 36 or (d) What is the entropy change of the universe (in J/K units)? (319)H.W) 1013.25 J of heat energy is supplied to 1mol of NH3 (2) which is initially volume is 4L at constant pressure 2 atm. if the process is isothermally expansion, determine its final volume. (3)
- One mole of an ideal gas initially kept in a cylinder at pressure 1 MPa and temperature 27°C is made to expand until its volume is doubled. (a) How much work is done if the expansion is (i) adiabatic (ii) isobaric (iii) isothermal? (b) Identify the processes in which change in internal energy is least and is maximum. (c) Show each process on a PV diagram. (d) Name the processes in which the heat (Take y = 5/3 and R=8.3 J mol-1 K-1)P2.30 A 1.75 mol sample of an ideal gas for which Cv.m = 3R/2 undergoes the following two-step process: (1) From an initial state of the gas described by T = 15.0°C and P = 5.00 X 104 Pa, the gas undergoes an isothermal ex- pansion against a constant external pressure of 2.50 × 104 Pa until the volume has doubled. (2) Subsequently, the gas is cooled at constant volume. The temperature falls to -19.0°C. Calculate q, w, AU, and AH for each step and for the overall process.(a) Suppose that attractions are the dominant interaction between gas molecules, and the equation of state is p = nRT/V – n2a/V2. Determine the work (W(non-ideal gas)) of reversible, isothermal expansion of such a gas from initial volume V (initial) = 20.0 L to final volume V(final) = 40.0 L if n = 2.00 mol, T = 300 K, and a = 3.621 atm-L2/mol2. Watch your units. (b)Determine the work (W(ideal gas) of reversible, isothermal expansion of an ideal gas from initial volume V (initial) = 20.0 L to final volume V(final) = 40.0 L if n = 2.00 mol and T = 300 K. (c) Show the difference W(non-ideal) – W(ideal). If all your calculations are done correctly, this result shows you the effect of attractive interaction between gas particles on the work done by the system.