Water in a 6-ft^3 closed, rigid tank is at 200 F, 90 % quality. The tank is then cooled to 20

Water in a 6-ft^3 closed, rigid tank is at 200 F, 90 %...

Key Concepts

Closed, Rigid Tank

A closed, rigid tank is one where the mass is constant and the volume does not change during the process. This means that any change in the state of the fluid is due solely to heat transfer, making it an ideal system for applying energy balance concepts without work interactions associated with volume change.

Quality (Dryness Fraction)

Quality is the ratio of the mass of vapor to the total mass in a saturated liquid-vapor mixture. It is crucial for determining the properties of the mixture because knowing the quality allows one to calculate the specific internal energy and specific volume of the mixture from the saturated liquid and vapor properties.

Constant Volume Process

In a constant volume process, the volume remains fixed throughout the process. This constraint implies that any thermal energy change directly influences the state of the fluid and its properties, without compensating work done by or on the system. This is key when analyzing processes such as cooling or heating within a rigid vessel.

Phase Change in Water

Water undergoing a phase change, especially from a saturated mixture to a subcooled or compressed state, requires careful analysis of its thermodynamic properties. Understanding how properties like internal energy and specific volume change during phase transitions is fundamental for determining heat transfer in such processes.

Energy Analysis for Heat Transfer

Calculating the heat transfer in a thermodynamic process involves applying the first law of thermodynamics, which relates the change in internal energy to the heat added or removed from the system. In a rigid tank, since no work is performed (due to constant volume), the entire energy change is accounted for by the heat transfer.

Use of Steam Tables

Steam tables provide essential thermodynamic properties of water at various states, such as saturated and superheated conditions. They are used to obtain specific properties like internal energy and specific volume for both liquid and vapor phases, which are necessary for accurately analyzing the state and energy changes in the system.

Transcript

00:01 All right guys, we are given the following data for water in rigid tag that is t1 is equal to 200 degree fahrenheit.

00:10 We've got t2 is equal to 20 degrees fahrenheit.

00:14 We've got x1 is equal to 0 .9 and we've got v1 is equal to 6 cubic feet.

00:21 So from superheated water table f7 .1 corresponding to temperature t1, we can obtain the saturation and evaporation -specific volume and internal energy.

00:31 That is vf is equal to 0 .1663 cubic fit per lbm and we've got vfg is equal to 33 .6146 cubic fit per lbm.

00:53 Then we've got uf is equal to 168 .03 btu per lbm and we've got ufg.

01:09 Is equal to 906 .15 btu per lbm.

01:17 Now guys, calculating the initial specific internal energy, that is, u1 is equal to uf plus x1 into ufg, that is equal to 168, 168 .103 plus 0 .9 into 906 .159 into 906 .151 .5 ,000, and 0 .03 plus 0 .9 into 906 .151 .05 .0 .0 .0 .0 .9 into is equal to 983 .5 .56b .m.

01:57 So calculating the initial specific volume, we have v1 is equal to vf plus x1 into vfg, that is equal to 0 .01663 plus 0 .9 into 33 .6463 plus 0 .9 into 33 .646666 .6 .6 .6.

02:19 And that is equal to 30 .27 cubic fit per lbm.

02:27 So calculating mass, we've got m is equal to v1 over small v1, that is the specific volume.

02:38 So we have 6 over 30 .27 is equal to 0 .2lbm.

02:46 So water in rigid tank, water is in rigid tank, so volume remains constant.

02:51 That is v2 is equal to v1 is equal to 30 .27 cubic fit per lbm.

02:59 So in constant volume process, work done is equal to zero.

03:05 So we have w is equal to zero from saturated, solid saturated vapor table f7 .4 corresponding to temperature t2, that is equal to 20 degree fahrenheit.

03:19 Heights, we can obtain saturation solid and evaporation specific volume and internal energy...

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