Question

In: Physics

1. you are given a .5 m^3 container containing 9 moles of an ideal diatomic gas...

1. you are given a .5 m^3 container containing 9 moles of an ideal diatomic gas at 0° C, and you want to allow it to reach room temperature (20° C) while staying at the same pressure. You have a choice of holding the volume constant while heating it (process A) and then slowly decompressing the gas isothermally (process B) or simply heating it while maintaining pressure (process C).

a) What is the pressure of the gas?

b) What is the change in internal energy of the gas in going from the initial state to the final state?

c) Calculate the work done and heat transferred during process A. note whether these transfer energy into or out of the gas.

d) Calculate the work done and heat transferred during process B. note whether these transfer energy into or out of the gas.

e) Calculate the work done and heat transferred during process C. note whether these transfer energy into or out of the gas.

f) How do the total work and heat transfer compare for the two methods for getting from the initial state to the final state (AB and C)?

Expert Solution

PV = nRT

a) V1=0.5m³

n= 9 moles

T1 = 0 ^oC = 273 K

T2 = 20 ^oC = 293 K

a) P= nRT/V = 9*8.314*273/0.5 = 40854.99 Pa

b) Change in internal energy, E_int = nC_vT

C_v = (5/2)R, for diatomic gas

E_int = 9*(5/2)*8.314*20 = 3741.3 J

c) Work done = 0 at constant volume

heat transferred = change in internal energy = 3741.3 J

d) At constant temperature, W = -nRTln(V2/V1) =-9*8.314*273*ln(0.54/0.5) = -1572.12 J

Heat Transferred = -Work Done = 1572.12 J

e) At constant pressure,

Work done= -PV

P2 = P1 =P

V2/V1 = T2/T1

V2 = (293/273)*0.5 = 0.54 m³

V = 0.54-0.5 = 0.04 m³

Work done, W_C = -40854.99*0.04 = -1634.2 J

Heat Transferred, Q_C = change in internal energy-work done = 3741.3+1634.2 = 5375.5 J

e) Total work done in process AB, W_AB = -1572.12 J

Total heat transferred in process AB, Q_AB = 3741.3 + 1572.12 = 5313.42 J

So, W_AB > W_C

Q_AB < Q_C

genius_generous answered 19 hours ago

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