Truck cylinder, ideal gas law problem

AI Thread Summary
The discussion revolves around a problem involving a diesel engine cylinder, where air is compressed, and the final temperature and volume need to be determined. The initial conditions include a volume of 500 cm^3, a temperature of 30°C, and a pressure of 1.0 atm. The user successfully calculated the final temperature to be 1100°C but struggled to find the final volume. After some attempts, they resolved the volume using the work formula related to pressure and volume changes. The conversation highlights the application of the ideal gas law and work-energy principles in thermodynamics.
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Homework Statement



One cylinder in the diesel engine of a truck has an initial volume of 500 cm^3. Air is admitted to the cylinder at 30 C and a pressure of 1.0 atm. The piston rod then does 450 J of work to rapidly compress the air. What is its final temperature? What is its final volume?

Homework Equations



PV = nRT
\Delta Eth = (5/2)nR\DeltaT

The Attempt at a Solution



I found the temperature using the second equation to be 1100 C which is right. However i cannot find the final volume for the life of me. I tried P\gamma - 1T-\gamma and use the final pressure to find the volume but that didn't seem to work. Is there another way to go about this?
 
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finally figured it out using the formula:

W = PV\gamma(Vf1-\gamma - Vi1-\gamma)/(1 - \gamma)
 
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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