# 1 kg of fluidis compressed reversible according to law pv=25, where p is in bar and v is in m^3/kg. The final volume is 1/4 of the initial volume. Calculate the work done on the fluid , and sketch the p-v diagram

The work done on a fluid is the integral of pressure with respect to volume, W=∫p dv. Since we are dealing with a reversible process according to the law pv=25, it follows that v/p^2=constant (1/25). We can then use this information to determine the work done on the fluid.

First, using the given data we can calculate the initial and final volumes: vi = 4Vf or Vf = vi/4 = 1m³/(4kg) . The next step is to calculate ΔW by taking the integral of pdv from vi to Vf which yields: ∫_vi^Vf pdv = 25*ln(vi)-25*ln(Vf) = 25*ln(4)-25*ln(1/4)= 400 ln 2 J.

### 1 kg of fluidis compressed reversible according to law pv=25, where p is in bar and v is in m^3/kg. The final volume is 1/4 of the initial volume. Calculate the work done on the fluid , and sketch the p-v diagram

We can also sketch out a pressure-volume diagram for this process. Starting at point A (1m³/kg, 25bar), we would move along an horizontal line until point B (0.25m³/kg, 6.25bar). This represents an isothermal compression process since temperature remains constant during compression as per Charles’ Law for ideal gases. The area under this curve represents 400J as calculated above (W=-ΔU).

In conclusion, when compressing 1 kg of gas reversibly according law PV=C where C constant value work done equal integral pressure respect volume from initial final volumes In example provided 400 ln 2 Joules required compress original state quarter its size Additionally sketching P-V graph helpful visualizing understand dynamics involved Moreover understanding basic equations fundamental physics applicable real world scenarios demonstrate importance studying subject Mascetti 2020

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