An astronaut visiting Mars leaves a canister of 1.25 moles of ideal diatomic nitrogen gas of mol mass: 4.56 x 10-26 kg on Mars' surface. Mars has no atmosphere, a mass of 7.35 x 1022 kg and a radius of 1.74 x 106 m. 1. If the canister is cylindrical, comprising of a radius of 0.150 m and a length of 0.450 m, with a nitric pressure of 1.00 x 105 Pa: a) What is the magnitude of force that the nitrogen gas applies to the canister walls? b) Show that the temperature of the gas is 306K. 2. If a piston inside the canister moves compressing the gas in an isothermic process, increasing the pressure of gas by a factor of 5.00, what is the change in entropy of the gas as a result? 3. Work out how the most likely speed of a molecule in the canister is 426 ms-1 b) If you start with an expression for gravitational potential energy, show the minimum vertical velocity required for a particle on the surface of Mars to escape into space is 2.37 x 103 ms-1. c) If the lid is opened by the astronaut, can any of the leaking molecules escape into space? Discuss your thoughts.
An astronaut visiting Mars leaves a canister of 1.25 moles of ideal diatomic nitrogen gas of mol mass: 4.56 x 10-26 kg on Mars' surface. Mars has no atmosphere, a mass of 7.35 x 1022 kg and a radius of 1.74 x 106 m.
1. If the canister is cylindrical, comprising of a radius of 0.150 m and a length of 0.450 m, with a nitric pressure of 1.00 x 105 Pa:
a) What is the magnitude of force that the nitrogen gas applies to the canister walls?
b) Show that the temperature of the gas is 306K.
2. If a piston inside the canister moves compressing the gas in an isothermic process, increasing the pressure of gas by a factor of 5.00, what is the change in entropy of the gas as a result?
3. Work out how the most likely speed of a molecule in the canister is 426 ms-1
b) If you start with an expression for gravitational potential energy, show the minimum vertical velocity required for a particle on the surface of Mars to escape into space is 2.37 x 103 ms-1.
c) If the lid is opened by the astronaut, can any of the leaking molecules escape into space? Discuss your thoughts.
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