A 2-m^3 storage tank contains 95 % liquid and 5 % vapor by...

A $2-m^{3}$ storage tank contains $95 \%$ liquid and $5 \%$ vapor by volume of liquified natural gas (LNG) at $160 \mathrm{K},$ as shown in Fig. $\mathrm{P} 6.134 .$ It may be assumed that LNG has the same properties as pure methane. Heat is transferred to the tank and saturated vapor at $160 \mathrm{K}$ flows into the steady flow heater, which it leaves at $300 \mathrm{K}$. The process continues until all the liquid in the storage tank is gone. Calculate the total amount of heat transfer to the tank and the total amount of heat transferred to the heater.

Key Concepts

Two-Phase Equilibrium

This concept refers to the co?existence of two phases, typically liquid and vapor, under a given set of conditions in a system. In thermodynamics, it is important to understand how the properties of a mixture are determined by the distribution between these phases, and how parameters like quality (mass fraction of vapor) and saturation conditions relate to equilibrium states.

Phase Change and Latent Heat

Phase change involves the transformation of a substance from one phase to another, such as from liquid to vapor, without a change in temperature during the process. The latent heat is the energy required for this change, and it is a critical factor when calculating the total energy input necessary for vaporizing a given amount of liquid.

Energy Balance in Closed Systems

This key concept involves applying the first law of thermodynamics to a closed system where mass remains constant but energy enters or leaves the system in the form of work or heat. In problems involving phase change in a tank, it is essential to account for the heat required not only to vaporize the liquid but also for any sensible energy changes in the system.

Steady Flow Energy Equation

The steady flow energy equation is used to analyze devices through which mass flows continuously, such as heaters, compressors, and turbines. It relates the enthalpy changes of the fluid to the heat transfer and work interactions, allowing the determination of the energy required to raise the fluid's temperature from an initial to a final state in a steady-flow process.

Transcript

00:02 A storage tank contains liquefied natural gas, lng, which is at 95 % liquid and 5 % vapor by volume, at a given temperature.

00:13 The lng has the same properties as pure methane.

00:17 Heat is transferred to the tank and the saturated vapor at this temperature then flows into a heater and leaves at a higher temperature.

00:25 Now the process continues until all the liquid in the storage tank is gone.

00:29 We want to calculate the total amount of heat transfer to the tank and the total amount of heat transfer to the tank.

00:33 Amount of heat transferred to the heater.

00:37 So let's first take our control volume to be the tank.

00:48 Now we have flow out of the tank and this is a transient process.

00:52 So we'll first write our continuity equation as follows.

00:59 The mass of the gas or the mass at the end the final state m2 minus the initial mass m1 must equal to the mass that is exit to the tank and entered the heater.

01:18 We can then write the energy equation as well and the energy equation is the heat transfer to the tank q tank which we wish to calculate must equal to the difference in internal energies of the final state minus the initial state plus the energy of the gas that is exited m -e -h -e.

01:47 So if we take our temperature at 160 kelvin, we can go to our tables and we can first find the mass of the liquid mf to be the total volume v over the specific volume v and so this is the total volume 0 .95 times 2 95 % over the specific volume we're using methane here 0 .00297 and so we get the mass of fluid to be 600 and 39 .73kg and then we can do the similar process and find the mass of the gas.

02:38 So the vapor mass again is the total volume of the vapor capital g, v over the specific volume little v and so this is 0 .055 times 2 or 5 % over the specific volume of 0 .0 .0 .0.

03:02 3935 and so the mass of vapor is 2 .541 kg.

03:11 So now we have the mass of the fluid and the mass of the gas...

Please give Ace some feedback