Question

An insulated tank contains air at 0.5 atm pressure and 298K. The outside pressure is at 1 atm pressure and 298K. A valve is opened and air is allowed to ow into the tank. The air inside and outside the tank behaves ideally. What is the temperature of the gas in the tank after it is lled?

Answer 1

The temperature of the gas after it is filled is 596 K

Step-by-step explanation:

According to Gay-Lussac law, the pressure of a gas mass is directly proportional to temperature to a constant volume. That means than if pressure rise, the temperature too. We can assume then the volume is constant because the tank is isolated. The tank will be full when pressure will be in equilibrium, that means when pressure will be 1 atm because it is environment pressure. Using the following equation:

P1 /T1 = P2 /T2 and replacing, T2 = P2 *T1 / P1 = 1 atm * 298K / 0.5 atm = 596 K.

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