6. In this problem, we will study the relationship between pressure, temperature, and volume for an ideal gas. Consider an ideal gas in a closed container. You can assume the number of molecules (or equivalently, the number of moles) is constant. Which of the following statements is true? Give an explanation for each. a. If the pressure and the volume of the gas both double, the temperature of the gas must double. b. If the volume of the gas doubles during an isobaric (constant pressure) expansion, the temperature stays unchanged. c. If the temperature doubles, at least one of the volume or pressure must increase. Arigid container holds 2.0 g of helium (4g/mol) at an initial temperature of 300 K on one side of a barrier and 10.0 g of (diatomic) nitrogen (28g/mol) at an initial temperature of 600 K on the other side. a. We might approximate that the two gases exchange heat only with each other until they come to equilibrium. How might this condition be achieved in a practical setup? b. Find the final temperature, the amount of energy transferred from one gas to the other, and the direction the energy is transferred. c. What is the total thermal energy in the final state within each gas: E He, EN2- d. What are the initial rms speeds of the molecules Vrms,He,i, Vrms,N2,? What are the final rms speeds, Vrms,He,f, Vrms,N2,f? Show that the ratio of the final speeds of the two gasses is 4/28. Why? e. What is the final translational kinetic energy per molecule in each gas? Express your answer in units of electron-volts (eV), where lev = 1.6 x 10-19]