Solving for volume in Van der Waals Equation?

AI Thread Summary
To determine the specific volume of water steam at 100 kPa and 500 degrees Celsius, the Van der Waals equation is applied after initially using the ideal gas law, yielding a specific volume of 3.57 m^3/kg. The user expresses confusion regarding how to isolate volume (v) in the Van der Waals equation. They have successfully rearranged the equation but are still struggling to solve for specific volume. Further assistance is requested to clarify the steps needed to isolate v in the context of the Van der Waals equation. The discussion highlights the challenges faced when transitioning from ideal gas calculations to real gas behavior using Van der Waals.
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Solving for volume in Van der Waals Equation??

Homework Statement


Determine the specific volume, v (volume per mass[m^3/kg]) of a water steam at a pressure of 100kPa and a temperature of 500 degrees Celsius by assuming an ideal gas (pV = nRT) and by using the van der Waals equation for n moles


Homework Equations


pv = nRT
van der waals equation (p + n^2a/V^2)(V-nb) = nRT


The Attempt at a Solution


alright I got the first part no problem as i used the molar mass of air to be 18.0g/mol and I got the specific volume to be 3.57 m^3/kg. The second part of the question is confusing me because I have no clue how to solve for the volume for Van der Waals! any help please?
 
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well I was able to get Van Der Walls Equation in terms of specific volume:

(p + a/(v^2M^2)) (v- b/M) = RT/M

still can't figure out how to solve for v, specific volume?
 
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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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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...
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