Find the change in the Kinetic energy of an Ideal Gas

[Dr Dr news]

You need to clarify the problem statement. How do you get from the initial state to the final state?

 

[Helly123]

You need to clarify the problem statement. How do you get from the initial state to the final state?

Hmm..
The volume doubled and pressure 0.3 lower than before. Gases do work. But in adiabatic condition Q = 0
$\Delta$U = W
So Ek = W?

 

[Helly123]

case 2) Without going into the gory detail, for an adiabatic process, p(V)^γ = con, where γ = c(p)/c(V) = 1.67 for a monatomic gas. which means that
p1(V1)^γ = p2(V2)^γ = (p1/1.3)(2 V1)^γ; 1.3 ≠ (2)^1.67. This is some unknown process - not adiabatic.

Is this related to number 2? Or what?

 

[Dr Dr news]

The volume doubling as the pressure decreases by 30$ is not an adiabatic process. Ref. #24.

 

[Helly123]

You need to clarify the problem statement. How do you get from the initial state to the final state?

This is the full questions. Hope it still readable

 

[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