Calculating Work Done by a Gas Using the PV=1000 Equation | Thermo Help

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To calculate the work done by a gas expanding under the equation PV=1000, the appropriate formula is net flow work = p2v2 - p1v1. The pressure drops from 1000 kPa to 500 kPa, leading to a calculated work output of 693.1 kJ/kg. The confusion arises from whether to use the work equation w = -PΔV, but since the force is not constant, the net flow work formula is more suitable. Understanding the relationship between pressure and specific volume is crucial for accurate calculations. Proper application of these principles will yield the correct work done by the gas.
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A gas expands according to the equation pv=1000. where p is pressure in kPa and v is specific volume m^3/kg. If the gas pressure drops from 1000 to 500kPa, how much work was done by the gas??

Ok I am new to thermo and given a question and can't figure it out.
Do I use net flow work = p2v2-p1v1??
Answer is 693.1 kJ/kg.

or is it w-p delta v?
I am not sure.
Any help or direction would help thanks
 
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Start from
work = force x displacement
BUT remember that the force is not constant.
 

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