How Is Work Calculated in Isothermal Compression of Air?

[icnhoj]

1. Calculate the work done in compressing isothermally 2kg of dry air to one-tenth its volume at 15C



2. Work= the integral of pressure times the change in volume, the limits of integration being the initial and final volumes, v1 and v2.



3. The equation is very general, and doesn't have a variable for mass of the air parcel. The problem also doesn't have a value for p, so I don't know if I am supposed to have a solution with p as a variable in it...

 

[Dick]

Just set up the integral leaving variables where you don't know something. You may find the answer doesn't depend on things you don't know.

 

[m2003]

I would first clarify any uncertainties about the problem. I would ask for more information, such as the pressure and initial volume of the air parcel, to ensure that I have all the necessary variables to solve the problem accurately. Once I have all the information, I would use the ideal gas law to calculate the pressure of the air parcel at the given temperature of 15C. Then, using the given information of compressing the air parcel to one-tenth its volume, I would calculate the final volume. With all the necessary variables, I would then use the given equation of work to solve for the work done in compressing the air parcel isothermally. I would also double-check my calculations and units to ensure the accuracy of my answer. Additionally, I would mention the assumptions made in this calculation, such as assuming the air parcel behaves ideally and that the compression is done slowly enough to maintain a constant temperature. Overall, my response would include a thorough and precise solution to the problem, while also acknowledging any limitations or assumptions made in the calculation.