The ideal gas law derived the ideal gas law, discovered experimentally, is an equation of state that relates the observable state variables of the gas--pressure, temperature, and density (or quantity per volume): pv=nkbt (or pv=nrt), where n is the number of atoms, n is the number of moles, and r and kb are ideal gas constants such that r=nakb, where na is avogadro's number. in this problem, you should use boltzmann's constant instead of the gas constant r. remarkably, the pressure does not depend on the mass of the gas particles. why don't heavier gas particles generate more pressure? this puzzle was explained by making a key assumption about the connection between the microscopic world and the macroscopic temperature t. this assumption is called the equipartition theorem. the equipartition theorem states that the average energy associated with each degree of freedom in a system at absolute temperature t is 12kbt, where kb=1.38×10−23j/k is boltzmann's constant. a degree of freedom is a term that appears quadratically in the energy, for instance 12mv2x for the kinetic energy of a gas particle of mass m with velocity vx along the x axis. this problem will show how the ideal gas law follows from the equipartition theorem. to derive the ideal gas law, consider a single gas particle of mass m that is moving with speed vx in a container with length lx along the x direction. (figure 1) part a find the magnitude of the average force 〈fx〉 in the x direction that the particle exerts on the right-hand wall of the container as it bounces back and forth. assume that collisions between the wall and particle are elastic and that the position of the container is fixed. be careful of the sign of your answer. express the magnitude of the average force in terms of m, vx, and lx. 〈fx〉 = mvx2lx submithintsmy answersgive upreview part correct part b imagine that the container from the problem introduction is now filled with n identical gas particles of mass m. the particles each have different x velocities, but their average x velocity squared, denoted 〈v2x〉, is consistent with the equipartition theorem. find the pressure p on the right-hand wall of the container. express the pressure in terms of the absolute temperature t, the volume of the container v (where v=lxlylz), kb, and any other given quantities. the lengths of the sides of the container should not appear in your answer. p = m submithintsmy answersgive upreview part part c this question will be shown after you complete previous question(s). part d this question will be shown after you complete previous question(s). provide feedbackcontinue figure 1 of 1 no title provided ph105-s004 spring 2016