Thermodynamics Ideal Gas Problem

AI Thread Summary
The discussion revolves around calculating the work done by an ideal gas during an expansion from state (p_1, V_1) to (p_2, V_2), where p_2 is double p_1 and V_2 is double V_1. The initial attempt involved using a formula for work that led to an error due to an incorrect numerical multiplier. A suggestion was made to visualize the process on a pressure vs. volume plot, indicating that the work done corresponds to the area under the line connecting the two states. Ultimately, the problem was solved by correctly calculating this area. The key takeaway is to focus on the geometric interpretation of work in thermodynamics rather than solely relying on equations.
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Homework Statement


An ideal gas expands from the state (p_1, V_1 ) to the state (p_2, V_2 ), where p_2 = 2p_1 and V_2 = 2V_1. The expansion proceeds along the straight diagonal path AB shown in the figure.

Find an expression for the work done by the gas during this process.
Express your answer in terms of the variables p_1 and V_1.


Homework Equations


W = (p_1 V_1 - p_2 V_2) / (y - 1)

The Attempt at a Solution


I put the equation exactly with y = 1.4.
Masteringphysics says "Your answer either contains an incorrect numerical multiplier or is missing one.".

What have I done wrong?
 
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Is that an equation from a textbook? Don't think about trying to apply an equation. Instead, use theory and some common sense.

You state in the problem that there is a figure that you don't show. It does sound like you have a pressure vs volume plot where there is a straight line from p1,V1 to p2,V2.

With that, work is basically the area under that line. Calculate that area for work.
 
I have managed to solve this problem. Thank you.
 
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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