8. A thermally isolated quantity of gas with an initial volume of 10.5 liters is

Question

8. A thermally isolated quantity of gas with an initial volume of 10.5 liters is compressed isobarically at a pressure of 265 kPa. If 910 J of work is done on the system, what is the final volume of the gas? liters 9. The work done by two moles of a monatornic ideal gas ( 53) in expanding adiabatically is 830 J. The initial temperature and volume of the gas are 365 K and 0.140 m. W hat is the final volume of the gas? [Hint: For an adiabatic process => Tyr-T -1] m3 10. A nuclear power plant operates at 65 percent of its maximum theoretical (Carnot) efficiency between temperatures of 520°C and 290°C. If the plant produces electric energy at the rate of 1.30 Giga-Watts, how much exhaust heat is discharged per hour? Joules

Explanation / Answer

8)

work done = P*dV = P*(vf - vi)

P = 265*10^3 pa

vi = 10.54*10^-3 m^3

W = 910 J

910 = 265*10^3*(vf - 10.54*10^-3)

vf= 0.0139 m^3 = 0.0139*1000 liters

vf = 13.9 liters

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9)

work in adiabatic process W = n*R*(T2-T1)/(r - 1)

830 = 2*8.314*(T2-365)/((5/3)-1)

T2 = 398.3 K

T1*v1^(r-1) = T2*v2^(r-1)

365*0.14^(5/3-1) = 398.3*v2^(5/3-1)

v2 = 0.123 m^3

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10)

maximum efficiency nmax = 1 - Tc/Th

nmax = 1- (290+273)/(520+273) = 0.29

efficiency of power plant n = 0.65*nmax = 0.1885

energy discharged E = n*P*t

E = 0.1885*1.3*10^9*3600

E = 882.18*10^9 J

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