A 0.3-m^3 rigid tank is filled with saturated liquid water at 200^∘ C. A valve at the bottom of

A 0.3-m^3 rigid tank is filled with saturated liquid water...

A $0.3-\mathrm{m}^{3}$ rigid tank is filled with saturated liquid water at $200^{\circ} \mathrm{C}$. A valve at the bottom of the tank is opened, and liquid is withdrawn from the tank. Heat is transferred to the water such that the temperature in the tank remains constant. Determine the amount of heat that must be transferred by the time one-half of the total mass has been withdrawn.

Key Concepts

Energy Balance with Mass Transfer

When mass is withdrawn from a system, the energy balance must account for both the energy associated with the removed mass and any heat added to maintain the system’s conditions. This analysis, based on the first law of thermodynamics for a closed system with mass transfer, is crucial for determining the required heat transfer to maintain a constant temperature during mass removal.

Rigid Tank

A rigid tank is a container of fixed volume where no boundary work is performed during a process because the volume does not change. This constraint means that any energy changes in the system are solely due to heat transfer and internal energy changes, not mechanical work associated with volume change.

Isothermal Process

An isothermal process is one that occurs at constant temperature. In thermodynamic analyses, this implies that any heat added to or removed from the system must exactly balance the energy change associated with work or mass transfer to keep the system's temperature unchanged.

Saturated Liquid Properties

Saturated liquid properties refer to the thermodynamic state where a liquid is in equilibrium with its vapor at a given temperature and pressure. These properties, such as specific volume, internal energy, and enthalpy, are critical in analyzing processes involving phase change or the removal of mass from a saturated system.

Transcript

00:01 Hi everyone.

00:01 So what we have is a rigid tank of volume 0 .3 cubic meters with saturated water that's at 200 degrees celsius and this rigid tank has a valve at the bottom.

00:12 So what we're asked to find is the heat transfer for when one half of the mass inside the tank has been taken out and we are assuming that this is an isothermal process.

00:23 So what we know is the volume of this tank is equal to zero.

00:32 0 .3 cubic meters and the initial temperature is equal to 200 degrees c.

00:40 It is saturated water and the total mass leaving is going to be one half the initial mass that's inside and we're asked to find the total heat transfer.

00:52 So what we can do actually is just go to our tables, table a4 for saturated water and at t equals 200 degrees celsius we know that these specific volume is going to be equal to 0 .001157 cubic meters per kilogram.

01:12 We'll also know that specific internal energy u is equal to 850 .46 kilojoules per kilogram.

01:27 And we also can solve for age, and we know that specific enthalpy is 852 .26 kilojoules per kilogram.

01:38 Now, all of these quantities are of the, basically this is bf, uf, and hf in the table, and the reason why it is because we are dealing with saturated water.

01:51 So we can go ahead and use the f term.

01:56 What we can do now is solve for the initial mass inside the tank.

02:00 Now, we can just use that the mass is equal to the total volume over the specific volume, and we know quantities and we can do this off from m1 and that gives us a mass of 259 .29 kilograms.

02:16 Now we're going to do a mass balance.

02:18 So our system is going to be defined as the rigid tank.

02:23 So what that means is the mass coming in side of the tank minus the mass leaving the tank is equal to the change in mass of the system.

02:32 Now we have no mass coming in, right? but we do have mass leaving and we're going to call that m e.

02:38 So that next.

02:39 Negative m .e is going to be equal to the change in mass of the system...

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