Pressure change with constant volume

AI Thread Summary
The discussion revolves around a thermodynamics problem involving two moles of a gas undergoing an isochoric process where the pressure is doubled from 2 Atm to 4 Atm. Participants are trying to determine the change in temperature (ΔT), the work required, and the change in internal energy of the gas. The first law of thermodynamics is applied, noting that under constant volume, the entire energy spent on heating translates into internal energy change. There is uncertainty about whether the ideal gas law can be assumed for solving the problem, with requests for hints on relating temperature change to pressure without this assumption. The conversation highlights the complexities of thermodynamic equations in constant volume scenarios.
SadStudent
Messages
7
Reaction score
0

Homework Statement


Given two moles of some gas with two atoms per molecule which has energy U=aK_{B}T.
Assume the initial pressure is P_{i}= 2 Atm and the initial volume is P_{i}= 0.001\ m^{3}.
Now we heat it in an isochoric process to 2P_{i}.

What would be \Delta T?
What would be the work required to do that?
What would be the change in the gas particles' internal energy?

Homework Equations


U=aK_{B}T
dU=PdS-TdV

The Attempt at a Solution


Well using the first law of thermodynamics, I got that under constant volume dV=0 so \frac{dQ}{dT}=\frac{\partial U}{\partial T} so the entire energy that we spent on heating would be transferred into the gas.
What's a tricky to me is to formulate the change in temperature as a function of pressure because dV=0 so I'd really welcome a hint.

Thanks!
 
Last edited:
Physics news on Phys.org
SadStudent said:

Homework Equations



dU=PdS-TdV

Oops, check that.

What's a tricky to me is to formulate the change in temperature as a function of pressure because dV=0 so I'd really welcome a hint.

Can you assume the gas obeys the ideal gas law?
 
TSny said:
Oops, check that.Can you assume the gas obeys the ideal gas law?

And yes of course it was a typo :) it's supposed to be dU=TdS-PdV

I'm really not sure whether I can, is there a way of solving this without this assumption?
 
Last edited:

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

Calculate ideal-gas temperature of a material
Replies
2
Views
2K
Find Isobaric Expansion & Pressure-Volume Coefficient for Solid
Replies
4
Views
1K
Is enthalpy just the sum of internal energy and work against external pressure?
Replies
5
Views
987
Air pressure changes in a vessel as the vessel volume increases
Replies
8
Views
967
Trouble solving for end state of two control volumes in a rigid tank
Replies
12
Views
2K
Entropy and the Helmholtz Free Energy of a Mass-Piston System
Replies
8
Views
2K
Gas in mercury manometer, finding its normal volume
Replies
2
Views
2K
Internal energy of a container filled with water & steam
Replies
12
Views
2K
Gas temperature in a constant volume
Replies
8
Views
2K
Percentage change in the density of a gas
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top