Two copper cylinders, immersed in a water tank at 50.1°C contain helium and nitr

Question

Two copper cylinders, immersed in a water tank at 50.1°C contain helium and nitrogen, respectively. The helium-filled cylinder has a volume twice as large as the nitrogen-filled cylinder.
a) Calculate the average kinetic energy of a helium molecule at 50.1°C.
b) Calculate the average kinetic energy of a nitrogen molecule at 50.1°C.
c) Determine the molar specific heat at constant volume (CV) and at constant pressure (Cp) for helium. Enter CV first. Give answer in J/mol·K.
d) Determine the molar specific heat at constant volume (CV) and at constant pressure (Cp) for nitrogen. Enter CV first. Give answer in J/mol·K.
e) Find ? (gama) for helium.
f) Find ? (gama ) for nitrogen.

Explanation / Answer

a) helium is monoatomic so 3/2 k T=1.5*1.38E-23*(50.1+273)=6.69E-21J
b) nitrogen is diatomic so 5/2 k T=1.11E-20 J
c) helium is monoatomic so Cv=3/2 R=12.5 J/mol K
Cp=Cv+R=20.8 J/mol K
d) hydrogen is diatomic so Cv=5/2 R= 20.8 J/mol K
Cp=Cv+R=20.8+8.3=29.1 J/mol K
e) =Cp/Cv=5/2R/3/2 R=5/3

f) =Cp/Cv=7/2R/5/2R=7/5

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