Title 11 Temperature and Ideal Gas Tutorial Solution.pdf ✅

St. Andrew’s Junior College H2 Physics 11-2 Question 2: Relationship between Kinetic Theory & Temperature In a mixture of two monoatomic gases X and Y in thermal equilibrium, the molecules of Y have twice the mass of those of X. The mean translational kinetic energy of the molecules of Y is 6.0 × 10-21 J. What is the ratio of the mean-square speed of Y to the mean-square speed of X? Guided working: For X, we can write down this equation: 1⁄2 mX = 3 2 kTX --- (1) Write down the corresponding equation for Y: 1⁄2 mY = 3 2 kTY --- (2) The question says that “the molecules of Y have twice the mass of those of X”. Does this mean: mX = 2 mY or 2mX = mY ? Pls circle the correct expression. The question says that “gases X and Y in thermal equilibrium”. What does this tell us about TX and TY ? TX = TY Now, place equation (2) over equation (1), and solve for 2 2 Y X c c     : ( ) ( ) 2 1  2 1 3 2 2 1 2 2 3 2 Y Y Y m c X X X m c T kT k   =   2 2 1 3 (2 ) 2 2 1 3 2 2 X Y X X X X m c kT m c kT   =   2 2 Y X c c     = 1⁄2 = 0.5