What is the equation for adiabats in a P-V plane?

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The discussion revolves around finding the equation for adiabats in the P-V plane, emphasizing that an adiabat represents a process with no heat transfer. Participants clarify that in an adiabatic process, the work done equals the change in internal energy, and the equation of state should relate pressure and volume. There's confusion about how to express this relationship mathematically, particularly regarding the role of temperature changes. The conversation suggests that understanding the internal energy equation and its dependence on pressure and volume is crucial for deriving the desired equation. Overall, the focus is on clarifying the mathematical representation of adiabatic processes in thermodynamics.
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I have in front of me an equation for energy in a system [ U=U(P,V) ]. I'm being asked to find "the equation of the adiabats in the P-V plane". What are they looking for? I know an adiabat is a system with no heat transfer, meaning that the energy of the system would equal the work done on the system. But what is this equation that they are looking for?
 
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well, I'm guessing that if you have U in terms of P, V, solve for P and substitute \Delta U =C_v \Delta T for U (first putting it in the form \Delta U)...the equation of the P,V graph? An equation for P?
 
I don't think that will help with anything. If it's an adiabatic process, deltaT will be zero.
 
no, for an adiabatic process q is zero, the work of an adiabat is equal to the change in its internal energy, the work is equal to constant volume internal energy, the equation I've shown above.

you better get studying

also post the exact problem
 
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}...
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