Two closed vessel A and B of equal volume containing air at pressure P1 and temperature T1 are connected to each other through a narrow open tube.If the temperature of one is now maintained(where T1>T2) then that what will be the final pressure of air
To determine the final pressure of air in the connected vessels, we can apply the principles of Boyle's Law and Dalton's Law of Partial Pressures.
1. Boyle's Law states that at a constant temperature, the product of pressure and volume is constant. This means that if we have two vessels of equal volume connected, the total volume will remain the same throughout the process.
2. Dalton's Law of Partial Pressures states that in a mixture of gases, the total pressure is equal to the sum of the partial pressures of each gas. In this case, we have only one gas, which is air.
Now let's go step-by-step to find the final pressure of air:
Step 1: Understand the given data:
- Vessel A and B have equal volume.
- Vessel A is initially at pressure P1 and temperature T1.
- Vessel B is initially at an unknown pressure P2 and temperature T2.
- The temperature of vessel A is maintained at T1.
Step 2: Apply Boyle's Law:
Since the volume of vessels A and B is equal, and vessel A's temperature is maintained at T1, we can use Boyle's Law to relate the initial pressure of vessel A, P1, to the final pressure of the connected vessels, which we'll call Pf:
P1 * V = Pf * V
V is the common volume and can be canceled out on both sides of the equation:
P1 = Pf
Step 3: Apply Dalton's Law of Partial Pressures:
According to Dalton's Law, the total pressure in the connected vessels will be the sum of the partial pressures of each vessel. Since vessel A's pressure remains unchanged, the final pressure in the connected vessels will be:
Pf = P1 + P2
Putting it all together, we can conclude that the final pressure of air in the connected vessels is:
Pf = P1 + P2
However, without knowing the initial pressure P2 or any other relevant information, we cannot determine the final pressure of air accurately.