An ideal gas is compressed from an initial volume V₀ to a final volume V₀ 2 starting from the same initial state (P₀, V₀) . The compression is carried out along two different paths, represented by curves A and B on a P-V diagram. If curve A lies above curve B (i.e., curve A ends at a higher pressure than curve B), which of the following correctly identifies the two processes?

Step-by-step solution

The slope of a P-V curve is given by dP dV . For an isothermal process, the slope is - P V . For an adiabatic process, the slope is - P V . Since > 1 , the adiabatic curve is steeper than the isothermal curve. During compression, the volume decreases. Starting from the same initial state, the steeper adiabatic curve will rise more rapidly than the isothermal curve. Therefore, the adiabatic curve will lie above the isothermal curve on the P-V diagram, reaching a higher final pressure. Since curve A ends at a higher