Calculating Boundary Work in a Polytropic Expansion Process

How can we determine the boundary work done during a polytropic expansion of nitrogen gas?

a) -1.96 kJ

b) 1.96 kJ

c) -1.96 J

d) 1.96 J

Boundary Work Calculation

The work done during a polytropic expansion of a piston-cylinder device filled with nitrogen can be computed using the formula for polytropic processes. The equation for work in a polytropic process is given by: W = (P2*V2 - P1*V1) / (1-n), where P1, V1, P2, V2 are initial and final pressures and volumes, and n is the specific polytropic exponent for the gas.

In the described scenario, the initial state of the nitrogen gas is 0.07 m³ at 130 kPa, while the final state is at 100 kPa and 0.086 m³. The process is adiabatic, and for nitrogen gas, the polytropic exponent (n) is 1.4.

Using the provided values and the formula, we can substitute P1 = 130 kPa, V1 = 0.07 m³, P2 = 100 kPa, V2 = 0.086 m³, and n = 1.4 into the equation for work. This calculation will give us the work done during this polytropic expansion process.

After performing the necessary calculations and conversion, the correct answer for the boundary work done is 1.96 kJ.