Сосуд объемом V1=6 л, заполненный идеальным газом при давлении p1= 1,4·10^5 Па, соединили с пустым сосудом объемом V2= 40 л. Определите установившееся давление p газа после того, как установилась начальная температура.
The most important equation to use in this scenario is the ideal gas law: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to calculate the number of moles of gas in the first vessel. Using the given pressure of 1.4*105 Pa and the volume of 6L, we can rearrange the ideal gas law to solve for n. This gives us n = (PV)/(RT) = ((1.4*105 Pa)(6L))/((8.31 J/mol*K)(273.15K)) = 0.00202 mol.
Next, we need to use the combined gas law to calculate the final pressure once the two vessels are connected. The combined gas law is P1V1/T1 = P2V2/T2, where subscripts 1 and 2 represent the initial and final conditions, respectively.
Since we already know the initial conditions for V1, P1, and T1, we can plug in those values and solve for P2. Using V2 = 40L and assuming the temperature stays constant, we get P2 = (P1V1V2)/(V1V2) = ((1.4*105 Pa)(6L)(40L))/(6L+40L) = 1.29*104 Pa.
So, the final pressure of the combined gas will be 1.29*104 Pa, or approximately 0.13 atmospheres.
This result may seem counterintuitive since the original pressure was much higher, but remember that we are now dealing with a larger volume due to the combined vessels. The gas molecules are now spread out, causing the pressure to decrease.
