Question

60 puncte+coroana
VA ROG
8. O canitate niu=1 mol de gaz ideal monoatomic ocupa volumul V1=10 Lla presiunea p1=100 kPa. La incalzire gazul s-a dilatat la presiunea contanta pana la volumul V2=30 L , dupa care presiunea lui a crescut de 2 ori la volum contant . Determinati
a) temperatura gazului in starea initiala , la sfarsitul transoformari izobare si la sfarsitul celei izocore
b) lucrul mecanic efectuat de gaz
c) variatia energiei interne a gazului
d) cantitatea de caldura comunicata gazului

Answer 1

a)
p1V1=νRT1=>T1=p1V1/νR=10⁵*10*10⁻³/1*8,314≈12 K
p1=p2=p=constant
V1/T1=V2/T2=>T2=T1V2/V1=12*30*10⁻³/10*10⁻³=36 K
V1=V2=V= constant
p2=2p1=2*10⁵ Pa
p1/T1=p2/T2'=>T2'=T1*p2/p1=12*2*10⁵/10⁵=24 K

b)L=νRΔT=1*8,314*(T2-T1)=8,314(36-12)=8,314*24≈200 J

c)ΔU=νCvΔT+νCvΔT'=3/2*ν*R(T2-T1)+3/2*ν*(T2'-T1)=3/2(p2V2-p1V1)+3/2(p2V2-p1V1)=3/2*p(V2-V1)+3/2V(p2-p1)=3/2*10⁵*(30*10⁻³-10*10⁻³)+3/2*10*10⁻³(2*10⁵-10⁵)=1,5*10⁵*0,02+0,015*10⁵=3000+1500=4500 J

d)Q=νCpΔT+νCvΔT'=5/2*ν*R(T2-T1)+3/2νR(T2'-T1)=5/2(p2T2-p1T1)+3/2(p2V2-p1V1)= 5/2p(V2-V1)+3/2V(p2-p1)=5/2*10⁵(30*10⁻³-10*10⁻³)+3/2*10*10⁻³(2*10⁵-10⁵)=2,5*10⁵*0,02+3/2*10*10⁻³*10⁵=5000+1500=6500 J

Sper saa fie corect