question_answer

Compare the formula \[{{\mathbf{C}}_{\mathbf{P}}}\mathbf{ -}{{\mathbf{C}}_{\mathbf{V}}}\mathbf{=R}\] for an ideal gas with the thermodynamic relation \[\Delta U=\Delta Q-P\Delta V.\]

Answer:

                The equation \[\Delta U=\Delta Q-P\Delta V\] can be written as \[\Delta Q=\Delta U+P\Delta V\] This equation implies that when the heat \[\Delta Q\]is given to an ideal gas, a part of it is used in increasing the internal energy (\[\Delta U\]) and the remaining in doing work of expansion (\[P\Delta V\]). Similarly, the formula \[{{C}_{P}}-{{C}_{V}}=R\]can be written as \[{{C}_{P}}\Delta T={{C}_{V}}\Delta T+R\Delta T\] This equation implies that when the heat \[{{C}_{P}}\Delta T\]is given to an ideal gas at constant pressure, its one part is used in increasing the temperature or internal energy \[({{C}_{V}}\Delta \Tau .)\] and the other part in doing work against external pressure \[(R\Delta T).\]