1) A hot air balloon has a volume of 600m^3. It is filled with air at a temperature of 170oC. Find the net upwards force (considering the buoyant force and gravity), given that the density of air outside the balloon, which has a temperature of 10oC, is 1.25 kg/m^3.
2) Derive the Ideal Gas Law. Consider a particle of mass m and velocity v moving in a box with walls that are Lx apart in the x-direction, Ly apart in the y-direction, and Lz apart in the z-direction. Find the magnitude of the impulse that it exerts on a wall when it collides elastically with that wall. Next, find how long between two such collisions. Use this to determine the average force on the wall. Divide by the area of each wall to find the pressure on it. Next, note that if there are lots of particles, some will be moving more in the x-direction, some more in the y-direction, and so on, so, on average, Vx^2=Vy^2=Vz^2. How does this show that temperature is related to average kinetic energy for an ideal gas?
Thanks a lot for the help!! I've been trying these questions for so long and I just don't understand them.
2) Derive the Ideal Gas Law. Consider a particle of mass m and velocity v moving in a box with walls that are Lx apart in the x-direction, Ly apart in the y-direction, and Lz apart in the z-direction. Find the magnitude of the impulse that it exerts on a wall when it collides elastically with that wall. Next, find how long between two such collisions. Use this to determine the average force on the wall. Divide by the area of each wall to find the pressure on it. Next, note that if there are lots of particles, some will be moving more in the x-direction, some more in the y-direction, and so on, so, on average, Vx^2=Vy^2=Vz^2. How does this show that temperature is related to average kinetic energy for an ideal gas?
Thanks a lot for the help!! I've been trying these questions for so long and I just don't understand them.