Two closed vessels of equal volume both with pressure p1 and temperature t1 are connected to each other by tube with negligible volume. If the temperature maintained of both vessels is then changed to t1 and t2 respectively what is the pressure in the vessels?
To determine the pressure in the vessels after changing the temperature, we can make use of the ideal gas law.
The ideal gas law is given by the equation:
PV = nRT,
where P is the pressure, V is the volume, n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Since the two vessels are connected by a tube with negligible volume, the number of moles of gas remains constant. Therefore, we can write the initial and final equations using the ideal gas law as follows:
For the first vessel:
P1 * V = n * R * T1
For the second vessel:
P2 * V = n * R * T2
Since both vessels have equal volume (V1 = V2 = V), we can rewrite the equations as:
P1 = (n * R * T1) / V
P2 = (n * R * T2) / V
Given that V1 = V2 and T1 = T2, we can simplify the equations as:
P1 = (n * R * T1) / V
P2 = (n * R * T1) / V
Therefore, the pressure in both vessels will be equal and will remain the same as P1, regardless of the change in temperature from T1 to T2.
Pressure in vessel 1 is p1 since the temperature hasn't changed.
Pressure in vessel 2 is
p2 = p1 x (t2/t1)