A saturated air-water vapor mixture at 20^∘ C 100 kPa, is contained in a 5-m^3 closed tank in eq

A saturated air-water vapor mixture at 20^∘ C 100 kPa, is...

Key Concepts

Phase Equilibrium

This concept involves understanding how two phases (typically liquid and vapor) coexist in equilibrium under certain temperature and pressure conditions. It is based on the idea that at a given saturation temperature and pressure, the liquid and vapor phases have equal chemical potentials, allowing them to coexist without further net change. The analysis of phase equilibrium is crucial for determining the state of a substance when energy is added or removed, and for tracking phase transitions during processes such as heating or cooling.

Saturated Mixture and Quality

A saturated mixture consists of a substance existing in both liquid and vapor phases in equilibrium at a given temperature and pressure. The quality (or dryness fraction) defines the mass fraction of the vapor in the mixture. Understanding the quality is essential when assessing the phase composition, as it helps to determine how much of the substance is in the vapor phase versus the liquid phase. This in turn influences properties like specific volume and the energy required for phase changes.

Constant Volume Process

A constant volume process is one in which the volume of the system remains fixed throughout the process, such as in a closed rigid tank. In such processes, any heating or cooling results in changes in pressure and temperature rather than changes in volume. This scenario is especially important when evaluating thermodynamic processes because the work done by or on the system is zero (if only expansion work is considered), and all energy transfer must be accounted for via heat or changes in internal energy.

Energy Balance and Heat Transfer

The first law of thermodynamics is applied to perform an energy balance on a closed system, which involves calculating the change in internal energy based on the heat added or removed and any work interactions. In a constant volume process, since no boundary work is done, the change in internal energy is directly equated to the net heat transfer. This concept is fundamental for determining how much heat is required to drive a process, such as raising the temperature and possibly inducing phase changes in the system.

Transcript

00:01 Hi, everybody.

00:01 So this question is asking us, is there any liquid water at the final state, find the heat transfer in the process, okay? so first we need to do the volume of the liquid.

00:15 And we got one times 0 .001.

00:19 So we get 0 .001 meter cube.

00:23 And now we have the volume of the gas, which is v minus the liquid.

00:30 We're just going to make that l.

00:32 And so we have 5 minus 0 .001, and we get 4 .99 meter cubed.

00:41 And you could technically round it up to 5, but let's just keep it at that.

00:45 So we have initial relatively humidity at 5 equals 100%.

00:52 And we have p1, the p liquid, equals the p gas of the initial state.

01:02 And here, that's going to be 2 .339k pascels.

01:10 And so we can find the absolute humidity at 1 as 0 .622 pv1 divided by p minus pv1.

01:21 So here we have 0 .622 and 2 .339, 100 minus 2 .330.

01:32 And we get 0 .0149 and that's the ratio and now we need to find the mass of air so we have massive air equals 100 minus 2 .339 okay and now we have 4 .999 999 so we have the volume okay and we have 0 .287 at times 20 plus 273.

02:02 15 and and that's just converting it to kelvin, the temperature of kelvin's.

02:05 So we get 5 .802 kilograms.

02:12 And now we need to find the mass of volume 1 equals this guy right here, the humidity times mass air.

02:25 And we get 0 .0149 times 5 .802.

02:33 And in this we get 0 .0864 kilograms.

02:39 Okay.

02:41 And now we can do the ideal gas ratio.

02:44 So we have pav1 divided by t1 equals pa2 v2.

02:52 T2...