Use the exact values you enter to make later calculations. A certain ideal gas h
ID: 1882498 • Letter: U
Question
Use the exact values you enter to make later calculations. A certain ideal gas has a molar specific heat of CV = H. A 2.99-mol sample of the gas always starts at pressure 1.25 x 10 Pa and temperature295 K For each of the following processes, determine the final pressure (P), the final volume (V), the final temperature (T), the change in internal energy of the gas (Fint), the energy added to the gas by heat (2), and the work done on the gas (w (i)The uas is healed al constant pressure to 405 K. kPa Q- (ii) The gas is heated at constant volume to 405 K. Atint = (Il The gas is compressed at constant temperature to 140 kPa. ka . Cint (iv) The gasis compressed adiabatically to 14 kPa. . kPa 2- Need Help?Read ItExplanation / Answer
Ans)
Cpm=7/2R
=(7/2)(8.314 J/gmol-K)
=29.099 J/gmol-K
Cvm=Cp-R =(7/2R)-(R)
=(5/2)R
=(5/2) (8.314 J/gmol-K)
=20.785 J/gmol-K
n=2.99mol
P1=1.25x105 Pa =1.233 atm
T1=295K=27C
(i)The gas is heated at constant pressure to 405K
a)Pf=P1=125KPa
c)Tf=405K
b)Vf=(V1)(P1/Pf)(Tf/T1)
V1=nxRx(T1/P1)
=(2.99)x(0.08206atm-L/gmol-K)(295/1.233)
V1=58.7L
Vf=(58.7)x(125/125)x(405/295)
Vf=80.59 L
d)H=nxcpmx(Tf-T1)
=2.99x29.099x(405-295)
=9570J
U= nxcvmx(Tf-T1)
=2.99x20.785x(405-295)
=6836J
f)W=P(Vf-V1)
=(1.25x105N/m2)(0.08059m3-0.0587m3)
W=2736J
e)Q=U+W
=6836+2736
Q=9572J
(ii)the gas is heated at constant volume to 405K
b)Vf=V1=58.7L
a)Pf=(P1)(V1/Vf)(Tf/T1)
=(1.25x105)(1.00)(405/295)
=171.6KPa
c)Tf=405K=132C
d)
U=nxCvmx(Tf-T1)
=(2.99)x(20.785)x(405-295)
=6836J
f)W=0 since constant volume
e)Q=U+Wf
=6836J+0J
Q=6836J
(iii)the gas is compressed at constant temperature to 140KPa
For isothermal compression from 100KPa to 140KPa
a)Pf=140KPa
b)Vf=(V1)(P1/Pf)(Tf/T1)
=(58.7)(100/140)(1)
=41.92L
c)Tf=T1=300K
d)U=0J
W=nRTx[ln(P1/P2)]
W=(2.99x8.314x300)xln(100/140)
W=-25089J
Work done on the gas =-(W)=25089J
Q=U+W=0+25089=25089J
Heat must be removed from the gas
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