question_answer 20)

                  Consider a cycle followed by an engine (Fig.)                 1 to 2 is isothermal 2 to 3 is adiabatic 3 to 1 is adiabatic.                 Such a process does not exist because. (a) Heat is completely converted to mechanical energy in such a process, which is not possible. (b) Mechanical energy is completely converted to heat in this process, which is not possible. (c) Curves representing two adiabatic processes don?t intersect. (d) Curves representing an adiabatic process and an isothermal process don?t intersect.                

Answer:

                  (a, c)                 (a) Since             \[{{(\Delta Q)}_{1\to 2}}+{{(\Delta Q)}_{2\to 3}}+{{(\Delta Q)}_{3\to 1}}={{(\Delta W)}_{t\to 2}},\]                 [as \[{{(\Delta Q)}_{1\to 2}}={{(\Delta W)}_{1\to 2}}\] for an isothermal change and \[{{(\Delta Q)}_{2\to 3}}={{(\Delta Q)}_{3\to 1}}=0\] for adiabatic changes.]                 Heat is thus completely converted into mechanical energy in such a process, which is not possible.                 (c) Curves representing an adiabatic process and an isothermal process intersect. Both the curves \[(2\to 3)\] and \[(3\to 1),\] which intersect at 3, are adiabatic curves.