question_answer

What happens to the change in internal energy of a gas during (i) isothermal expansion and (ii) adiabatic expansion?                     

Answer:

                (i) Isothermal expansion. Temperature  Remains constant during an isothermal change. As internal energy is a function of temperature only, so it will remain constant during an isothermal change. As           \[\Delta T=0,\]so \[\Delta U={{C}_{V}}\Delta T=0.\]  (ii) Adiabatic expansion. For an adiabatic change, \[\Delta Q=0,\] so from first law of thermodynamics, \[\Delta Q=\Delta U+\Delta W=0\] or \[\Delta W=-\Delta U\] During expansion, work is done by a gas i.e., \[\Delta W\] is positive. So \[\Delta U\] must be negative. Hence internal energy of a gas decreases during an adiabatic expansion.