Piston thermodynamics - find P, V and T

AI Thread Summary
A horizontal insulated cylinder contains a frictionless piston with 54L of monatomic ideal gas on each side, initially at 1 atm and 273K. Heat is added to the gas on the left side, causing the piston to compress the gas on the right side to 7.59 atm, which undergoes an adiabatic process. The final temperature on the right side is calculated to be 614K after determining the final volume to be 16L. The left side's final temperature can be found using the ideal gas equation, with the pressure on both sides being equal after the expansion. The discussion emphasizes the relationship between pressure and temperature in this thermodynamic scenario.
hadroneater
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Homework Statement


A horizontal insulated cylinder contains a frictionless non-conducting piston. On each side of the piston are 54L of the same monatomic ideal gas with the ratio of heap capatities (C_p/C_v) = gamma = 5/3 at 1atm and 273K. Heat is slowly supplied through an inserted heating element(negilible volume) to the gas on the left side of the chamber until the piston compressed the gas on the right side to 7.59atm. What is the temperature on the right side and the left side?


Homework Equations







The Attempt at a Solution


I recognized that for the right side of the piston, it goes through an adiabatic process for which no heat is involved. I found the volume after compression from the equation PV^gamma = constant. V_f = 16L. Then the temperature after compression is found using PV/T = constant and T_f = 614K.

For the left side where heat is added, I'm having trouble finding it out. I know that V_f = 92L. How do I find T_f though?
 
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What is the pressure on the left? You know its volume. So, you can figure out its temperature from the ideal gas equation.

AM
 
The pressure after expansion isn't given.
 
Last edited:
hadroneater said:
The pressure after expansion isn't given.
Ok. But you can easily figure it out. Think about it. How are the pressures on the left and right sides related?

AM
 
Oh! Is it equal?


Of course...stupid me. Thank you.
 
Last edited:
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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