Monatomic gas, Isochoric Process.

AI Thread Summary
In an isochoric process involving 1.46 moles of a monatomic ideal gas, the work done on the system is zero due to constant volume conditions. The change in internal energy is equal to the heat added, as per the equation Change in I.E. = Q + W. The average kinetic energy formula, KE = (3/2)kT, is used to calculate the change in internal energy based on the temperature difference. The initial calculations mistakenly considered the change in kinetic energy for a single molecule instead of accounting for the total moles of gas. Correcting this will yield the accurate values for internal energy change and heat transfer.
yaylee
Messages
22
Reaction score
0

Homework Statement



n = 1.46 moles of ideal gas are heated isochorically (at constant volume) from tepmerature To = 649 oC to temperature Tf = 1184 oC. Find:

a) Work done on the system.
b) Change in Internal Energy of the system.
c) The total heat, Q, added or removed from the system.

Homework Equations


Change in I.E. = Q + W
KE (avg) = T = 3/2kT, where k = 1.38 x 10^-26 kJ/K

The Attempt at a Solution



a) Since this is an isochoric system, work done is ZERO! (No issues here.)
b,c) Change in Internal Energy, therefore is equal to Q, by the first equation, Change in IE = Q + W.
So, we can calculate change in IE, by change in KE.

KE = (3/2kT) for a monatomic gas.
so, change in KE = 3/2(k)(Tfinal - Tinitial), = (3/2)(1.38E-26)(1500 K - 704K) = change in IE = Q = 1.65 x 10^-23.

Am I reading the problem incorrectly? Many thanks in advance once again!
 
Physics news on Phys.org
(3/2)kT is the average translational KE of just one molecule.
 
It appears you have calculated the change in KE for a single molecule of the gas.
Remember, you have 1.46 moles of gas to start with.
 
Thanks!
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Internal Energy of an Ideal Gas
Replies
4
Views
2K
Isobaric/isochoric (?) heating of an ideal gas
Replies
5
Views
4K
Heat and work when temperature increases by 1 degree
Replies
21
Views
3K
What Happens When Gas Expands at Constant Pressure?
Replies
12
Views
6K
Isobaric Process: Finding Q, E, W.
Replies
1
Views
7K
PV Diagram of Ideal Monatomic Gas Processes
Replies
4
Views
2K
I Irreversible Isochoric Process in a Cycle
Replies
8
Views
3K
How Is Internal Energy Calculated for an Ideal Gas Using Temperature Change?
Replies
1
Views
1K
Energy of a Gas in equilibrium with BB-radiation
Replies
9
Views
2K
Isobaric Process, finding Change in Internal Energy
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top