P2.19 An ideal gas described by T; = 275 K, P; = 1.10 bar, and V; = 10.0 L is heated at constant volume until P = 10.0 bar. It then undergoes a reversible isothermal expansion until P = 1.10 bar. It is then restored to its original state by the extraction of heat at constant pressure. Depict this closed-cycle process in a P-V diagram. Calculate w for each step and for the total process. What values for w would you calculate if the cycle were traversed in the opposite direction?
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From PV diagram we can calculate workdone of each process and total process.
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- . A 2.50 mole sample of a perfect gas for which Cv,m = 3R/2 (assume constant over T-range) undergoes the following two-step process: (1) from an initial state of the gas described by T = 13 ºC and P = 1.75 x 105 Pa, the gas undergoes an isothermal expansion against a constant pressure of 3.75 x 104 Pa until the volume has doubled. (2) subsequently, the gas is cooled at constant volume. The temperature falls to -24ºC. Calculate q, w, ∆U, and ∆H for each step and for the overall process.Two moles of an ideal gas with cP=72R= 29.10 J mol-1 K-1 are at initial pressure p1= 1 atm and temperature T1 = 295 K. The gas undergoes two different processes from this particular initial state (1) Heating under constant volume to a final temperature of 405 K. Calculate the quantities AU, AH, AS, q and w (2) Adiabatic and irreversible change at a final temperature of 100 K. Calculate the quantities AU, AH, AS, q and w (1) (2) AU ΔΗ AS 9 W1 mole of an ideal gas with CV,m = 5/2 R undergoes transformation either (I) or (II) from aninitial temperature (Ti) = 250 K and initial pressure (Pi) = 1.00 bar. CV,m denotes molar heatcapacity at constant volume.(I) 1 mol of gas undergoes a reversible adiabatic expansion until the final pressure (Pf) ishalf of its initial value. The surroundings are at 250 K and 0.500 bar.(II) 1 mol of gas undergoes an adiabatic expansion against a constant external pressure(Pex) of 0.500 bar until the final pressure (Pf) is equal to half of its initial value. Thesurroundings are at 300 K and 0.500 bar.a) Calculate the change in entropy of the system (ΔSsys) (in unit J K-1 ) for each (I) and (II). b) Calculate the change in entropy of the surroundings (ΔSsur) (in unit J K-1 ) for each (I) and (II). c) Calculate the total change in entropy (ΔStot) (in unit J K-1 ) for each (I) and (II). d) State which of the process [(I) or (II)] is a spontaneous process.
- 2.0 mol of CO2 gas (assumed to be a perfect gas with Cv,m = 28.8 JK-1mol-1) is in a cylinder with a massless piston of cross-section 100 cm2 at 10°C and 9.0 atm. The gas expands adiabatically against an external pressure of 1.5 atm until the piston moves 15 cm. Calculate (a) q; (b) w; (c) ΔU; (d) ΔT; (e) ΔS for this process.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.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
- Derive the following thermodynamic equation of state. au = -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 du Differentiate the equation dU = –PdV + TdS with respect to V while keeping T constant to obtain an expression for Use the following as necessary: P, S, T, V, and av as ASVī to represent nRT = V -P+T·ASVT Step 2 of 7 as Identify the relationship between and Use the following as necessary: P, S, T, V, and APTy to represent asOne mole of a monatomic ideal gas begins in a state withP 5 1.00 atm and T 5 300 K. It is expanded reversiblyand adiabatically until the volume has doubled; then it isexpanded irreversibly and isothermally into a vacuumuntil the volume has doubled again; and then it is heatedreversibly at constant volume to 400 K. Finally, it is compressed reversibly and isothermally until a inal state withP 5 1.00 atm and T 5 400 K is reached. Calculate DSsysfor this process. (Hint: There are two ways to solve thisproblem—an easy way and a hard way.)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)
- (c) An ideal monoatomic gas at 1 bar and 300 K is expanded adiabatically against a constant pressure of 0.5 bar until the final pressure is 0.5 bar. Given that the Cy is 1.5R, calculate (iii) (iv) enthalpy per mole. internal energy per mole.1) A sample containing 1.50 mol of an ideal gas with CV,m = 20.8 J K−1 mol−1isinitially at 230 kPa and 315 K. It undergoes a reversible adiabatic expansion until itspressure reaches 170 kPa. Calculate the final volume V2; the final temperature T2, andthe work w done by the system.Derivation Derive the following thermodynamic equation of state. au = -P + T avT 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. du = -P + av () as Differentiate the equation dU = -PdV + TdS with respect to V while keeping T constant to obtain an expression for av Use the following as necessary: P, S, T, V, and ASV7 to represent nRT (), - du av V -P+T·ASVT Step 2 of 7 dP Use the following as necessary: P, S, T, V, and APTV to represent ) Identify the relationship between and av. as -S+ΤΔΡΤV