Practice question

**Internal energy change** ΔU = Q - W, for same initial and final states ΔU same regardless of path, but Q and W differ, e.g., isothermal expansion from V₁ to V₂ ΔU=0 Q=W=n R T ln(V₂/V₁), adiabatic expansion between same volumes ΔU=-W, Q=0, different Q,W same ΔU if same T change, illustrating state vs path functions. An isothermal process is characterized by constant temperature ( T = constant ). For an ideal gas, this implies P V = constant , with heat exchange balancing work done. Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV, isothermal