Question

Unit mass of a fluid at a pressure of 8 bar , and with a specific volume of 0.5 m³/kg contained in a cylinder behind a piston expands reversibly to a pressure of 0.5 bar according to a law of p=c/v² , where c is a constant. calculate the work done during the process

Answer 1

The work done during the expansion process of a fluid following the law p=c/v² is calculated by integrating this expression over the change in volume. Find the constant c using the initial conditions and then solve the integral from the initial to the final volume to determine the work done.

Step-by-step explanation:

To calculate the work done during the reversible expansion of a fluid according to the law p=c/v², we can use the integral form of the work done for a quasistatic process. The work done by the system during expansion or compression can be given by the integral W = ∫ P dV, where P is the pressure and V is the specific volume. Given the expression for pressure p as a function of volume v, p = c/v², and the initial and final conditions, we can find the constant c using the initial conditions c = p·v². Afterward, we can compute the work using the integral:

W = ∫₁₀₈ ₀₅ c/v² dv

By substituting known values and solving the definite integral from initial volume V1 to final volume V2, the work done on or by the gas can be determined.