Find the change in the Kinetic energy of an Ideal Gas

[Dr Dr news]

The first question is straightforward. Since the kinetic energy/molecule is (3/2)kT, the kinetic energy/mol is NA (3/2)kT =(3/2)RT. Further, this means that you are considering a monatomic gas which we know from kinetic theory has c(V) = 3R/2 and c(p) = 5R/2. The second question is for a V=con process, Q=?, since dV=0, Wk=0, and ΔU = Q, but ΔU=nc(V)ΔT=Q. The third question is for a p=con process, Wk=?, ΔU=Q-Wk, Wk=Q-ΔU=nc(p)ΔT-nc(V)ΔT=[c(p)-c(V)]nΔT=nRΔT=pΔV. The fourth question is for ΔT=0, Δε(kinetic)=?, since ε(kinetic)∝T, Δε(k)=0, The fifth question is for Q=0 and V(final)=2V(initial), an adiabatic expansion, ΔT=? The confusing part is the listed pressure ratio of p(final)=0.7p(initial). If it is truly an adiabatic expansion the relation p(f)/p(i)=[V(i)/V(f)]^γ=(1/2)^1.67=0.314. Maybe this is what was meant, p(f)=0.314p(i), just poorly worded, in that case T(f)/T(i)=[V(i)/V(f)]^(γ-1)=(1/2)^0.67=0.629=ε(k,f)/ε(k,i).

 

[Helly123]

The first question is straightforward. Since the kinetic energy/molecule is (3/2)kT, the kinetic energy/mol is NA (3/2)kT =(3/2)RT. Further, this means that you are considering a monatomic gas which we know from kinetic theory has c(V) = 3R/2 and c(p) = 5R/2. The second question is for a V=con process, Q=?, since dV=0, Wk=0, and ΔU = Q, but ΔU=nc(V)ΔT=Q. The third question is for a p=con process, Wk=?, ΔU=Q-Wk, Wk=Q-ΔU=nc(p)ΔT-nc(V)ΔT=[c(p)-c(V)]nΔT=nRΔT=pΔV. The fourth question is for ΔT=0, Δε(kinetic)=?, since ε(kinetic)∝T, Δε(k)=0, The fifth question is for Q=0 and V(final)=2V(initial), an adiabatic expansion, ΔT=? The confusing part is the listed pressure ratio of p(final)=0.7p(initial). If it is truly an adiabatic expansion the relation p(f)/p(i)=[V(i)/V(f)]^γ=(1/2)^1.67=0.314. Maybe this is what was meant, p(f)=0.314p(i), just poorly worded, in that case T(f)/T(i)=[V(i)/V(f)]^(γ-1)=(1/2)^0.67=0.629=ε(k,f)/ε(k,i).

Wow. Thanks a lot for reviewing all questions

 

[Helly123]

The first question is straightforward. Since the kinetic energy/molecule is (3/2)kT, the kinetic energy/mol is NA (3/2)kT =(3/2)RT. Further, this means that you are considering a monatomic gas which we know from kinetic theory has c(V) = 3R/2 and c(p) = 5R/2. The second question is for a V=con process, Q=?, since dV=0, Wk=0, and ΔU = Q, but ΔU=nc(V)ΔT=Q. The third question is for a p=con process, Wk=?, ΔU=Q-Wk, Wk=Q-ΔU=nc(p)ΔT-nc(V)ΔT=[c(p)-c(V)]nΔT=nRΔT=pΔV. The fourth question is for ΔT=0, Δε(kinetic)=?, since ε(kinetic)∝T, Δε(k)=0, The fifth question is for Q=0 and V(final)=2V(initial), an adiabatic expansion, ΔT=? The confusing part is the listed pressure ratio of p(final)=0.7p(initial). If it is truly an adiabatic expansion the relation p(f)/p(i)=[V(i)/V(f)]^γ=(1/2)^1.67=0.314. Maybe this is what was meant, p(f)=0.314p(i), just poorly worded, in that case T(f)/T(i)=[V(i)/V(f)]^(γ-1)=(1/2)^0.67=0.629=ε(k,f)/ε(k,i).

So, p f = 0.3 p i
Not that pf 0.3 lower than pi?

 

[Dr Dr news]

That is what it looks like to me.

 

[Helly123]

That is what it looks like to me.

Ok. Thanks sir