A ball is projected from ground with a velocity v at an angle ๐œƒ to the vertical . On its path it makes an elastic collision with a vertical wall and returns to ground . The total time of flight of the ball is 2๐‘ฃ๐‘ ๐‘–๐‘›๐œƒ" " /๐‘” 2๐‘ฃ๐‘๐‘œ๐‘ ๐œƒ" " /๐‘” 2๐‘ฃ๐‘ ๐‘–๐‘›2๐œƒ" " /๐‘” 2๐‘ฃ๐‘๐‘œ๐‘ ๐œƒ" " /๐‘”

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Two rigid boxes containing different ideal gases are placed on a table . Box A contains one mole of nitrogen at temperature ๐‘‡_๐‘œ , while box B contains one mole of helium at temperature 7/3 ๐‘‡_๐‘œ . The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes and heat exchange will happen only between boxes ) . Then the final temperature of the gases in terms of ๐‘‡_๐‘œ is 7/3 ๐‘‡_๐‘œ 3/2 ๐‘‡_๐‘œ 5/2 ๐‘‡_๐‘œ 3/7 ๐‘‡_๐‘œ

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