Saturated-liquid benzene at pressure P1=10 bar(T1^sat =451.7 K) is throttled in a steady-flow p

Saturated-liquid benzene at pressure P1=10 bar(T1^sat =451.7...

Saturated-liquid benzene at pressure $P_1=10 \mathrm{bar}\left(T_1^{\text {sat }}=451.7 \mathrm{~K}\right)$ is throttled in a steady-flow process to a pressure $P_2=1.2$ bar $\left(T_2^{\text {sat }}=358.7 \mathrm{~K}\right)$, where it is a liquid/vapor mixture. Estimate the molar fraction of the exit stream that is vapor. For liquid benzene, $C_P=162 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. Ignore the effect of pressure on the enthalpy of liquid benzene.

Key Concepts

Throttling Process

A throttling process is a type of steady-flow process in which a fluid passes through a restriction or valve, undergoing a significant drop in pressure. During this process, there is no work done by or on the fluid and negligible heat transfer, which results in an essentially constant enthalpy (isenthalpic process).

Isenthalpic Process

In an isenthalpic process, the total enthalpy of the fluid remains constant from inlet to outlet. This assumption is crucial in analyzing throttling and expansion processes since it allows the enthalpy at the higher pressure state to be equated to the enthalpy at the lower pressure state, even when phase change occurs.

Quality of a Two-Phase Mixture

Quality refers to the fraction (by mass or moles) of vapor in a liquid-vapor mixture. In thermodynamics, it is used to quantify the degree of vaporization in a mixture and is determined by balancing the sensible heat added to the liquid with the latent heat required for vaporization.

Sensible Heat and Specific Heat Capacity

Sensible heat is the energy transferred to or from a substance that results in a change in temperature without a phase change. Specific heat capacity is the measure of the amount of heat required to raise the temperature of a unit quantity of a substance by one degree. It is used to calculate the energy needed to reach a certain temperature when pressure effects on enthalpy are neglected.

Latent Heat of Vaporization

Latent heat of vaporization is the amount of energy required to convert a unit quantity of liquid into vapor at constant temperature and pressure. This energy is absorbed during the phase change and is critical for determining how much of the liquid converts into vapor in processes like throttling, where the enthalpy remains constant.

Transcript

00:01 In the given question, we have to calculate the pressure of benzene if the moles are one, okay, for a molar volume.

00:08 The volume is provided us as 2 liter.

00:10 The moles are 1.

00:12 Okay.

00:13 And we have to calculate this pressure utilizing the redlich -kion equation, which is p equals to nrt, v minus n b minus n square a under root t, 1 upon v, v, v plus n -n -r -t.

00:30 B.

00:31 Okay.

00:31 So we have been provided the temperature also that is t which is equal to 595 kelvin.

00:38 So we have to determine the pressure of benzene using this equation and we have to at the end determine what are the forces between the benzene are they attractive or they repulsive.

00:50 The value of a constant is provided us as 452 bar decometer to the power 6 mole minus 2 kelvin 1 by 2 and the value of constant b is given as 0 .0 8271 decameter cube mole inverse.

01:13 Now this pressure we are referring as pr and to calculate that we also need the value of this gas constant r.

01:22 So the value of capital r which is the universal gas constant is 0 .0 .831 decameter cube bar kelvin inverse, mole inverse, okay? so whenever our volume is in decameter cube and the pressure is in bar, we use the value of universal gas constant as 0 .0831.

01:44 So we can calculate this pr, moles are 1, gas constant 0 .0831 into our temperature that is 595 upon volume that is provided us as 2 liter.

02:00 Okay so 2 liter is also equal to 2 decameter cube okay 1 liter is equal to 1 degameter cube so we can use 2 liter as 2 decameter cube okay so volume is 2 over n that is the mole is 1 the value of b is 0 0 8271 subtracting n square 1 square a is 452.

02:28 Root temperature means root 595 into 1 upon v that is 2.

02:33 2 plus nb once again 1 into the value of b is you can write it here.

02:40 This is our 2 into 2 plus 1 into 0 .08271...

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