A 70 liter tank containing an ideal gas at a pressure of 40 atmospheres is connected by a valve to a 30 liter tank of an ideal gas at 70 atmospheres. The valve is opened slowly and the gases in two tanks mix. Assuming the temperature throughout is constant, what is the final pressure in the tanks?
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To find the final pressure in the tanks, we can use the principle of the combined gas law. The combined gas law states that for a given amount of gas, the initial pressure times the initial volume divided by the initial temperature is equal to the final pressure times the final volume divided by the final temperature.
In this case, we are assuming that the temperature throughout is constant. Therefore, the combined gas law simplifies to:
(P1 * V1) = (P2 * V2)
Where:
P1 = initial pressure of the first tank
V1 = initial volume of the first tank
P2 = initial pressure of the second tank
V2 = initial volume of the second tank
Given:
P1 = 40 atm
V1 = 70 liters
P2 = 70 atm
V2 = 30 liters
Now, let's plug in the values into the equation and solve for the final pressure:
(40 atm * 70 L) = (P2 * (70 L + 30 L))
Simplifying the equation:
2800 atm*L = (P2 * 100 L)
Now we can solve for P2 by dividing both sides of the equation by 100 L:
2800 atm*L / 100 L = P2
P2 = 28 atm
Therefore, the final pressure in the tanks when the gases mix is 28 atmospheres.