A thick-walled insulated metal chamber contains n, moles of helium at high pressure P;. It is connected through a valve with a large, almost empty gasholder in which the pressure is maintained at a constant value P', very nearly atmospheric. The valve is opened slightly, and the helium flows slowly and adiabatically into the gasholder until the pressure on the two sides of the valve is equalized. Prove that d oio-ge sd SVed diod bS h'- u; fu Tolto iuesy sA. lu nf = number of moles of helium left in the chamber, | where In - M u, = initial molar internal energy of helium in the chamber, = final molar internal energy of helium in the chamber, and h' = u'+ P' (where u'= molar internal energy of helium in the gasholder; v'= molar volume of helium in the gasholder). %3D %3D %3D
A thick-walled insulated metal chamber contains n, moles of helium at high pressure P;. It is connected through a valve with a large, almost empty gasholder in which the pressure is maintained at a constant value P', very nearly atmospheric. The valve is opened slightly, and the helium flows slowly and adiabatically into the gasholder until the pressure on the two sides of the valve is equalized. Prove that d oio-ge sd SVed diod bS h'- u; fu Tolto iuesy sA. lu nf = number of moles of helium left in the chamber, | where In - M u, = initial molar internal energy of helium in the chamber, = final molar internal energy of helium in the chamber, and h' = u'+ P' (where u'= molar internal energy of helium in the gasholder; v'= molar volume of helium in the gasholder). %3D %3D %3D
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to the container is a capillary tube through which the gas may leak slowly
out to the atmosphere, where the pressure is Po. Surrounding the container
and capillary is a water bath, in which is immersed an electrical resistor. The
gas is allowed to leak slowly through the capillary into the atmosphere while
electrical energy is dissipated in the resistor at such a rate that the temperature
of the gas, the container, the capillary, and the water is kept equal to thát ôf
the outside air. Show that, after as much gas as possible has leaked out during
time interval t, the change in internal energy is
"4- au)°d 13 = NV
where vo is the molar volume of the gas at atmospheric pressure, E 1s the
potential difference across the resistor, and I is the current in the resistor.
4.9. A thick-walled insulated metal chamber contains n, moles of helium at
high pressure P;. It is connected through a valve with a large, almost empty
gasholder in which the pressure is maintained at a constant value P', very
nearly atmospheric. The valve is opened slightly, and the helium flows slowly
and adiabatically into the gasholder until the pressure on the two sides of the
valve is equalized. Prove that d ofioqe odi sm5155 0Jod
Svid diod brS 1
%3D
0000
number of moles of helium left in the chamber,
fu
In - 4 u
where
initial molar internal energy of helium in the chamber,
in
uf = final molar internal energy of helium in the chamber, and
TH OU
h' u'+ P'v (where u'= molar internal energy of helium in the
gasholder; v'= molar volume of helium in the gasholder).
%3D
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4.10. Regarding the internal energy of a hydrostatic system to be a function of T and
P, derive the following equations:
ne
+ P
dP.
+P
ƏT
+ LP
aP
ÕP ()
ne
= Cp- PVß.
omoler selom ent ai u oodw
zelom
(9)
ne
= PVx– (Cp- Cy)
%3D
(o)
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