Thermodynamics: finding work done

AI Thread Summary
In a closed system, 0.4kg of gas at 374K undergoes isothermal and reversible expansion from 1MPa to 300kPa, prompting a discussion on calculating the work done. Participants express uncertainty about the correct approach, with one seeking guidance on the differential work equation and its relation to external pressure. Clarification is provided that the problem requires integration of PdV for accurate results, countering the notion that it can be solved with basic algebra. The conversation emphasizes the importance of understanding the relationship between pressure and volume changes in thermodynamic processes. Overall, the discussion highlights the complexity of the problem and the need for a solid grasp of thermodynamic principles.
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Homework Statement



In a closed system 0.4kg of gas at 374K is expanded isothermally and reversibly from 1MPa pressure to 300kPa. Given that Cv = 718j/kg and R = 287j/kg, determine the work done.[/B]

Homework Equations


Not sure? I guess W = p*V?

The Attempt at a Solution


I honestly don't know how to solve this one.
 
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NB: I don't want anyone to do this for me, in case anyone thinks I'm trying to cheat. I just want someone to point me in the right direction because I honestly don't know where to begin figuring this out.
 
What is the equation for the differential work dW done by a gas on its surroundings in terms of the external force per unit area Pext and the differential change in volume dV? For a reversible process, how is the external force per unit area Pext related to the gas pressure?

Chet
 
Chestermiller said:
What is the equation for the differential work dW done by a gas on its surroundings in terms of the external force per unit area Pext and the differential change in volume dV? For a reversible process, how is the external force per unit area Pext related to the gas pressure?

Chet
Chet, I'm sure this is an algebra based physics question, not calculus.
 
DrewHizzy said:
Chet, I'm sure this is an algebra based physics question, not calculus.
Really. What makes you think so? This problem can not be solved correctly unless PdV is integrated, or the person has a formula for the result of the PdV integration.

Chet
 
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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