Ideal Gas Problem: Proving Coefficient of Volume Expansion

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The discussion focuses on deriving the coefficient of volume expansion for an ideal gas using the ideal gas law, pv=nrt. It emphasizes that this coefficient is equal to the reciprocal of the Kelvin temperature when expansion occurs at constant pressure. Participants suggest starting with the expression for the coefficient of volume expansion and examining the relationship between volume and temperature. The equation V = nRT/P is highlighted as a key point for further calculations. Understanding these relationships is crucial for solving the problem effectively.
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The pressure , volume , number of moles , and Kelvin temperature of an ideal gas are related by the equation pv=nrt, where r is a constant. Prove that the coefficient of volume expansion for an ideal gas is equal to the reciprocal of the Kelvin temperature if the expansion occurs at constant pressure
 
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please help guys I am so stressed out =(
 
can anyone please point me in the write direction
 
What definition or equation do you have for the coefficient of volume expansion? That would be a good place to start.
 
Luongo said:
The pressure , volume , number of moles , and Kelvin temperature of an ideal gas are related by the equation pv=nrt, where r is a constant. Prove that the coefficient of volume expansion for an ideal gas is equal to the reciprocal of the Kelvin temperature if the expansion occurs at constant pressure
Start with the expression for the coefficient of volume expansion. Since V = nRT/P, what is
\left(\frac{\partial{V}}{\partial{T}}\right)_{P}\right)?

AM
 
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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