You have two samples of helium gas at the same pressure in separate steel containers of the same volume. You want the number of collisions of helium atoms with the walls of container 1 to be twice the number of collisions of helium atoms with the walls of container 2. Assume ideal behavior.

a. How does the temperature in container 1 compare to the temperature in container 2? That is, which temperature is larger and by what factor? Explain your answer and support it mathematically.

b. If the number of collisions is different in each container, how can the pressure be the same? Provide a written explanation with mathematical support.