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 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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