00:01
Hi there, so for this problem we are told that natural gas as a mixture of 75 % of methane and 25 % of ethene by mass is flowing to a compressor with a temperature of 17 celsius degrees and a pressure, let's call it, this initial temperature and the initial pressure of 100 kilo pascal.
00:50
Now the reversible adiabatic compressor brings the flow to a pressure, a final pressure, that is equal to 350 kilo pascal.
01:04
So for this problem, we need to find the exit temperature and the needed work per kilogram flow.
01:20
So with that said, we know that this process is steady and adiabatic and reversible.
01:36
So assuming that the ideal gas measure in constant heat capacity, so we will need some values to determine first.
01:51
So because we know that the exit temperature is equal to the initial temperature times the exit pressure that we call also the final pressure divided by the initial pressure and that elevated to k minus 1 and this divided by k.
02:17
Now, we need to determine that value of k, so we can obtain this temperature, and also we know that the work exit and is equal to the specific heat with the pressure constant times the exit temperature minus the initial temperature.
02:43
So we need to determine these two values in here, the specific heat, and the constant.
02:49
Now with that set, first we need to obtain the gas constant r for the mixture.
03:03
So that will be the sum of the specific heat times the gas constant for each term in here.
03:14
So we will have 0 .75.
03:18
This accounts for the 70 % of methane and and that is in here.
03:27
And this times the gas constant for this, that we know for the case of methane, is 0 .5183.
03:39
And this plus the 0 .25 times the gas constant for ethane, which is 0 .2 ,770.
03:55
So by doing this product we obtain that the gas constant for this mixture of gases is 0 .4578 kilojoules per kilogram per kelvin.
04:15
Now we need to obtain the specific heat for the mixture so that will be the product between the specific heat and sorry, the percentage for each one, each gas, times the specific heat for each gas.
04:37
So for the first case, for methane, we have 0 .75 for the 75 % this times the specific heat for this gas, which we know is 2 .254, and this plus is 0 .254.
04:59
Times the specific heat for ethin, which is 1 .666.
05:10
So from this product in here and this sum, of course, we obtain a value of 2 .132 kilojoules per kilogram per kelvin...