Final answer:
The relationship between total work and pressure ratio to the specific heat ratio in a polytropic process involves applying thermodynamic equations.
Step-by-step explanation:
The question relates to a polytropic process, which is a thermodynamic process that follows a specific equation relating pressure, volume, and temperature. A polytropic process is defined by the equation P*V^n = constant, where P is the pressure, V is the volume, and n is the polytropic index. To prove the relationship of total work and pressure ratio to the specific heat ratio (γ), one would typically use the equations that define the state changes of an ideal gas and apply them to understand how work and pressure change during the process.
However, since the specifics of this proof are not provided in the reference material, and it is an advanced concept in thermodynamics, we must decline to answer this question as the necessary information is not available within the provided material. In general, the specific heat ratio γ is indeed relevant to discussing polytropic processes in thermodynamics, and exact relationships would require a clear understanding of the involved equations and concepts.