Consider air to be an ideal gas of diatomic nitrogen(with 5 degrees of motional
ID: 1836551 • Letter: C
Question
Consider air to be an ideal gas of diatomic nitrogen(with 5 degrees of motional freedom). What is the molar constant volume heat capacity,C_v, for air? (express your answer as a multiple of the gas constant, R.)______________What is the value of the ratio of heat capacities, y = C_p/C_v,for air?_____________A pisiton quickly compresses air, initially at 285 K and I atm, in a thermally insulated cylinder from a volume of 1.80 liters. What is the temperature of the compressed air?_______________What is the pressure of the compressed air?_____________How much work is done on the gas in this compression (consider well whether the answer is a positive or negative number.)_______________Is this compression a reversible process?Explanation / Answer
1.in diatomic molecules ,there are three translational degree of freedom,2 rotational degree of freedom.The remaining (3*2-5)=1 will be vibrational degree of freedom.
therefore,total average energy per molecule
Etotal=3*1/2RT+2*1/2RT+1/2RT+1/2RT=3/2RT+RT+RT=7/2RT
now Cv=(dE/dt)v=7/2R=7/2*8.314=28.1 JK^-1mol^-1
2.ratio of heat capacity for diatomic gas=Cp/Cv=1.15 as Cp-Cv=R
3.Relation b/w temp. and volume
T2/T1=(V1/V2)^y-1 This lead to calculate T2, as T1=285K,V1=1.80li,V2=.25li,y=1.15
hence T2=1.34 k
4. T2/T1=(P1/P2)^1-y/y
P2=(4.70*10^-3)^1/.13 atm