question_answer 40)

                  An insulated container containing monoatomic gas of molar mass m is moving with velocity \[{{\upsilon }_{0}}.\] If the container is suddenly stopped, find the change in temperature.

Answer:

                  Mass of gas, \[M=\mu \,m,\]  where \[\mu \] is the number of moles                 When container suddenly stops, loss in K.E.                 \[=\frac{1}{2}\,m\upsilon _{0}^{2}=\,\frac{1}{2}\,(\mu \,m)\upsilon _{0}^{2}\]              ?. (i)                 This loss in K.E. appears as heat energy. AT is the change is temperature, then                 \[\Delta \,U=\,\frac{f}{2}\,\mu \,R\,\Delta T\]                 Since gas is monoatomic, so \[f=3\]                 \[\therefore \] \[U=\frac{3}{2}\,\mu \,R\,\Delta T\]                        ?. (ii)                 From eqns. (i) and (ii), we get                 \[\frac{3}{2}\,\mu \,R\,\Delta T\,=\frac{1}{2}\,\mu \,m\,\upsilon _{0}^{2}\]                 \[\therefore \] \[\Delta T=\,\frac{m\upsilon _{0}^{2}}{3R}\]