question_answer

The total translational kinetic energy of the molecules of a gas having volume V and pressure P is \[\mathbf{500}\text{ }\mathbf{J}\]. What will be the total translational kinetic energy of the molecules of the same gas occupying the same volume V but exerting a pressure 2P?           

Answer:

                If E is the translational K.E. per unit volume, then                                                  \[P=\frac{2}{3}E\] or \[E=\frac{3P}{2}\] Total translational K.E. of volume V is \[EV=\frac{3PV}{2}=500J\] When pressure becomes 2P, total translational K.E. \[=2\times 500=\mathbf{1000J}\]