# Thermodynamics: h vs u and Quality?

• swraman
In summary, the solution uses the conservation of mass and energy to determine the final state of the two tanks after they come to thermodynamic equilibrium. They use the formula (Quality)*Uvapor + (1-quality)*Uliquid to find the internal energy and specific volume, and they use internal energy instead of enthalpy because there is no heat or work crossing the control surface.

#### swraman

Hi,

I am trying to understand the solution to a quiz I had, and am having trouble.

The question was:
Two well-insulated rigid tanks are connected by a valve. Tank A contains 5 kg of superheated steam at 800oC and 800kPa. Tank B contains 1 kg of saturated water mixture at 150oC and 30% quality. The valve is opened and the two tanks eventually come to thermodynamic equilibrium. Perform a thermodynamics analysis based on conservation of mass and energy to determine if there is any liquid in the final state.

The solution says:
KE=PE=W=Q=0
Conservation of Energy: Ei-Ef=ΔEsys=0 Therefore Ei=Ef. This becomes Ui=Uf or MA*UA+MB*UB=Mf*Uf

Tank A: VA=MA*vA=5kg x 0.618 m3/kg =3.09 m3
UA = 5kg x 3662.5 kJ/kg =18312.5 kJ

Tank B: VB=MB*vB=1kg x(0.3* 0.3924 m3/kg+0.7* 0.00109 m3/kg)=0.1184 m3
UB = 0.3x 2559.1 kJ/kg +0.7 *631.66 kJ/kg =1209.89 kJ

Total volume at equilibrium = 3.208 m3
Total mass= 6 kg

Specific volume= 3.208m3/6kg=0.5346 m3/kg

Total internal energy= 19522.39 kJ specific energy=3253.7 kJ/kg
(v, u) states falls into the superheated regime; there will be no liquid in the final state.

First off, why (when they solve for internal energy and specific volume) do thy use the formula (Quality)*Uvapor + (1-quality)*Uliquid ? This makes sense to me in my head, but it says no our text that the generic equation for u,h,or v is:
Y = Yliq + (Quality)*Ysat.vapor

so why don't they use it in this scenario?

Second, why do they use internal energy and not enthalpy?

Thanks

--a lost Mechanical engineering student

swraman said:
First off, why (when they solve for internal energy and specific volume) do thy use the formula (Quality)*Uvapor + (1-quality)*Uliquid ? This makes sense to me in my head, but it says no our text that the generic equation for u,h,or v is:
Y = Yliq + (Quality)*Ysat.vapor

so why don't they use it in this scenario?

Second, why do they use internal energy and not enthalpy?

Thanks

--a lost Mechanical engineering student
The equation you're trying to write: Y = Yliq + (Quality)*Ysat.vapor

... is off just a bit. The correct equation is: Y = Yf + X Yfg
Where Yf is the fluid property at 100% saturated liquid
and
Yfg is the difference between the fluid property at 100% saturated gas and 100% saturated liquid.

Regarding why not enthalpy, if you rewrite the first law it helps to clear this up. Normally, we write:
dU = dQ + dW

But for any control volume with flow in and out, we can also rewrite it:
dU = dQ + dW + dH
where
dH = (Uin + pVin) - (Uout + pVout)
Note that gas flowing into or out of a control volume does work pV so we say H = U + pV
(See ref: http://web.mit.edu/16.unified/www/FALL/thermodynamics/chapter_4.htm )

So if we apply this to the system with two separated tanks that has a control surface around both tanks, we find no heat or work crossing the control surface (dQ=0 and dW=0), nor do we find any flow across the control surface, so dH = 0. All we're left with is dU = 0 (or U1 + U2 = U3).

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## 1. What is the difference between enthalpy (h) and internal energy (u) in thermodynamics?

Enthalpy (h) is the total energy of a system, including the internal energy (u) and the energy required to overcome pressure and volume changes. It is often used in thermodynamic calculations involving heat transfer at constant pressure. Internal energy (u) is the energy contained within a system, including the kinetic and potential energy of its molecules. It is usually used in calculations involving work done at constant volume.

## 2. How do h and u change in different thermodynamic processes?

In an isobaric (constant pressure) process, there is no change in h, but u increases as heat is added to the system. In an isochoric (constant volume) process, there is no change in u, but h increases as work is done on the system. In an isothermal (constant temperature) process, both h and u remain constant as heat and work cancel each other out. In an adiabatic (no heat transfer) process, both h and u decrease as work is done on the system, resulting in a decrease in temperature.

## 3. What is the significance of the quality of a substance in thermodynamics?

The quality of a substance refers to the ratio of the mass of the substance in its vapor phase to the total mass of the substance. In thermodynamics, it is used to determine the behavior of a substance during phase change processes. For example, the quality of steam in a steam turbine determines its ability to do work and generate power.

## 4. How is the quality of a substance related to its enthalpy and internal energy?

The quality of a substance is directly related to its enthalpy and internal energy. As a substance undergoes a phase change, its enthalpy and internal energy change as well. The enthalpy change is directly proportional to the mass of the substance in its vapor phase, while the internal energy change is directly proportional to the mass of the substance in its liquid phase.

## 5. Can the quality of a substance ever be greater than 1 in thermodynamics?

No, the quality of a substance cannot be greater than 1 in thermodynamics. This would imply that the entire mass of the substance is in its vapor phase, which is not possible. The quality can only range from 0 to 1, with 0 representing a completely liquid substance and 1 representing a completely vapor substance.