Calculate Final volume and temperature of piston

In summary, the conversation discusses the process of compressing air in a diesel engine and how to find the final temperature and volume. The equations used are P1•V1/T1 = P2•V2/T2 and Eth = W + Q, and work is calculated through the integral of pressure in terms of volume. The conversation also touches on the difference between isothermal and adiabatic compression processes and how this information can be used to solve the problem.
  • #1
Jamie_Pi
18
0

Homework Statement


One cylinder in the diesel engine of a truck has an initial volume of 640 cm3. Air is admitted to the cylinder at 30°C and a pressure of 1.0 atm. The piston rod then does 500 J of work to rapidly compress the air. What are its final temperature and volume?

Homework Equations


I know that:
P1 • V1 / T1 = P2 • V2 / T2
Eth = W + Q
And I know that work is the integral of pressure in terms of volume, but I'm not sure how to find the final values based on what I'm given.

The Attempt at a Solution



I set up my equation as by converting everything to SI units, so:
P1 = 101325 Pa
V1 = 0.64 M3
T1 = 305.15 K

And I know that I should be able to find the final volume based on the work done, but I don't know how.
 
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  • #2
What is the difference between an isothermal and an adiabatic compression process ?
Which compression process is used in your engine ?
How can you use this information to solve the problem ?
 
Last edited:

FAQ: Calculate Final volume and temperature of piston

What is the formula for calculating the final volume and temperature of a piston?

The formula is V2 = (P1 x V1 x T2) / T1 x P2, where V2 is the final volume, P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.

How do you determine the initial and final pressure and temperature of a piston?

The initial pressure and temperature can be measured using a pressure gauge and a thermometer. The final pressure and temperature can be calculated using the ideal gas law (PV = nRT), where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

Can this formula be applied to any type of gas?

Yes, the formula can be applied to any type of gas as long as the initial and final pressure and temperature are known. However, the ideal gas law may not be accurate for all gases in all conditions, so it is important to consider any deviations from ideal gas behavior.

What units should be used for the variables in the formula?

The units used for pressure should be in pascals (Pa), volume in cubic meters (m³), temperature in Kelvin (K), and the gas constant (R) depends on the units used for pressure and volume. It is important to ensure that all units are consistent in the formula to get an accurate result.

Can this formula be used for any type of piston or only for specific types?

This formula can be used for any type of piston as long as the initial and final pressure and temperature are known. However, it is important to consider the specific conditions and properties of the piston and gas being used to ensure accuracy.

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