How to Solve for the Fractional Change in Temperature in an Adiabatic Process?

AI Thread Summary
The discussion revolves around solving for the fractional change in temperature in an adiabatic process, specifically relating it to the fractional change in pressure. The key equation used is PV^γ = constant, which is relevant for ideal gases. Participants clarify that the relationship between pressure and temperature can be expressed as dP/dT = nR/V, leading to the conclusion that dP/P equals dT/T. The original poster initially struggled with their solution but ultimately resolved the issue with assistance from others. The conversation emphasizes the mathematical relationship between temperature and pressure changes in an ideal gas context.
Gyroscope

Homework Statement


3.14
(0.5) How is the fractional change in temperature related to \frac{dT}{T} the fractional change in pressure \frac{dP}{P} ?
(IPhO 2006)

Homework Equations



PV^{\gamma}=\rm constant

The Attempt at a Solution



nC_vdT=-PdV (1), dV/dP=-nRT/(P^2)

If I substitute dV in the equation (1) it does not give the right result.

Can someone help me, please? :-p

Thanks my dear friends.
 
Physics news on Phys.org
It appears you are talking about an ideal gas? Then in
P=nRT/V
we see right away that P changes the same way as T. This is shown mathematically as

\frac{dP}{dT}=\frac{nR}{V},

\frac{dP}{P}=\frac{nRdT}{PV}=\frac{dT}{T}.
 
Thanks marcusl for your help. But you are wrong. :( I already solved it. Thanks anyway my dear friend.
 
Sorry! Glad you solved it.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Correct Derivation of the Adiabatic Condition? (PV Diagram)
Replies
4
Views
987
Work done in adiabatic process vs work done in isothermal
Replies
2
Views
2K
How to calculate initial pressure and temperature - adiabatic process
Replies
7
Views
2K
When do formulas for adiabatic processes apply?
Replies
1
Views
1K
Thermally insulated container with alternating series of walls
Replies
49
Views
2K
Adiabatic expansion with temperature-dependent gamma
Replies
1
Views
1K
Final temperature of an adiabatic process between two reservoirs
Replies
25
Views
4K
What is the entropy for an irreversible adiabatic process?
Replies
1
Views
2K
Thermodynamics: adiabatic compression
Replies
8
Views
2K
Adiabatic Temperature Change in Rising Air
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top