Defiance Drake, having checked that the bridge is currently a vacuum, needs to p

Question

Defiance Drake, having checked that the bridge is currently a vacuum, needs to pressurize the area in order to take control of the freighter. She finds a panel of environmental controls on the side of the door, that control the valve to an emergency atmospheric canister connected to the volume of the bridge. The gas in the canister is held at a constant 20 degrees Celsius, and has a pressure of 6 atmospheres. Opening the valve to the bridge results in a final volume 6 times that of the canister (that includes the volume of the canister), and a pressure of 1 atm. Is the final temperature of the bridge higher or lower than the initial temperature of the canister? Explain how you know this. You may assume that the bridge is fully evacuated of all particles before the valve is opened.

Explanation / Answer

T1 = 20+273 = 293 K V1 = v P1 = 6atm

T2 = T V2 = 6 v P2 = 1 atm

using the formula

P1V1/T1 = P2V2/T2

hence T2 = 1 x 6v x293 / 6v

= 293K = 20 degrees

= T1

hence the final temperature is equal to the initial temperature of the canister

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