A gas with adiabatic exponent y is compressed adiabatically from an initial state (P₁, V₁) to final state (P₁, V₁). (a) Show that the work done in this process is Y- W PiVi Vi = -1 Y-1 Vf (b) Evaluate the result numerically for one mole of helium gas initially at P= 1.0 atm and T = 300 K compressed to half its initial volume. (c) Compute the work done in an isothermal compression from the same initial point to half the initial volume. Explain the difference between the numerical results for work done in adiabatic and isothermal compression.

A gas with adiabatic exponent y is compressed adiabatically from an initial state (P₁, V₁) to final state (P₁, V₁). (a) Show that the work done in this process is Y- W PiVi Vi = -1 Y-1 Vf (b) Evaluate the result numerically for one mole of helium gas initially at P= 1.0 atm and T = 300 K compressed to half its initial volume. (c) Compute the work done in an isothermal compression from the same initial point to half the initial volume. Explain the difference between the numerical results for work done in adiabatic and isothermal compression.