How to Calculate and Solve for Dryness Fraction at Constant Volume Heating or Cooling | Enthalpy

Last Updated on July 12, 2022

The dryness fraction at constant volume heating or cooling is illustrated by the image below.

To compute for the dryness fraction at constant volume heating or cooling, four essential parameters are needed and these parameters are Specific Volume of Gas at Point 2 (V_g2), Specific Volume of Gas at Point 1 (V_g1), Superheated Steam Temprature (T_sup) and Saturated Temprature (T_s).

The formula for calculating dryness fraction at constant volume heating or cooling:

x = ^V_g2 T_sup / _Vg1 Ts

Where:

x = Dryness Fraction
V_g2 = Specific Volume of Gas at Point 2
V_g1 = Specific Volume of Gas at Point 1
T_sup = Superheated Steam Temprature
T_s = Saturated Temprature

Given an example;
Find the dryness fraction when the specific volume of gas at point 2 is 4, the specific volume of gas at point 1 is 9, the superheated steam temperature is 6 and the saturated temperature is 2.

This implies that;

V_g2 = Specific Volume of Gas at Point 2 =4
V_g1 = Specific Volume of Gas at Point 1 = 9
T_sup = Superheated Steam Temprature = 6
T_s = Saturated Temprature = 2

x = ^V_g2 T_sup / _Vg1 Ts
x = ^{4 x 6} / _{9 x 2}
x = ²⁴ / ₁₈
x = 1.33

Therefore, the dryness fraction is 1.33.

Calculating the Specific Volume of Gas at Point 2 when the Dryness Fraction, the Specific Volume of Gas at Point 1, the Superheated Steam Temperature and the Saturated Temperature is Given.

V_g2 = ^{x(V_g1 T_s)} / _Tsup

Where:

V_g2 = Specific Volume of Gas at Point 2
x = Dryness Fraction
V_g1 = Specific Volume of Gas at Point 1
T_sup = Superheated Steam Temprature
T_s = Saturated Temprature

Let’s solve an example;
Find the specific volume of gas at point 2 when the dryness fraction is 10, the specific volume of gas at point 1 is 4, the superheated steam temperature is 12 and the saturated temperature is 2.

This implies that;

x = Dryness Fraction = 10
V_g1 = Specific Volume of Gas at Point 1 = 4
T_sup = Superheated Steam Temprature = 12
T_s = Saturated Temprature = 2

V_g2 = ^{x(V_g1 T_s)} / _Tsup
V_g2 = ^10(4)(2) / ₁₂
V_g2 = ⁸⁰ / ₁₂
V_g2 = 6.67

Therefore, the specific volume of gas at point 2 is 6.67

Calculating the Specific Volume of Gas at Point 1 when the Dryness Fraction, the Specific Volume of Gas at Point 2, the Superheated Steam Temperature and the Saturated Temperature is Given.

V_g1 = ^{V_g2 T_sup} / _{x Ts}

Where:

V_g1 = Specific Volume of Gas at Point 1
x = Dryness Fraction
V_g2 = Specific Volume of Gas at Point 2
T_sup = Superheated Steam Temprature
T_s = Saturated Temprature

Let’s solve an example;
Find the specific volume of gas at point 1 when the dryness fraction is 8, the specific volume of gas at point 2 is 4, the superheated steam temperature is 12 and the saturated temperature is 2.

This implies that;

x = Dryness Fraction = 8
V_g2 = Specific Volume of Gas at Point 2 = 4
T_sup = Superheated Steam Temprature = 12
T_s = Saturated Temprature = 2

V_g1 = ^{V_g2 T_sup} / _{x Ts}
V_g1 = ^(4)(12) / ₍₈₎₍₂₎
V_g1 = ⁴⁸ / ₁₆
V_g1 = 3

Therefore, the specific volume of gas at point 1 is 3.

Calculating the Superheated Steam Temperature when the Dryness Fraction, the Specific Volume of Gas at Point 2, the Specific Volume of Gas at Point 1 and the Saturated Temperature is Given.

T_sup = ^{x(V_g1 T_s)} / _Vg2

Where:

T_sup = Superheated Steam Temprature
x = Dryness Fraction
V_g2 = Specific Volume of Gas at Point 2
V_g1 = Specific Volume of Gas at Point 1
T_s = Saturated Temprature

Let’s solve an example;
Find the superheated steam temperature when the dryness fraction is 14, the specific volume of gas at point 2 is 4, the specific volume of gas at point 1 is 3 and the saturated temperature is 2.

This implies that;

x = Dryness Fraction = 14
V_g2 = Specific Volume of Gas at Point 2 = 4
V_g1 = Specific Volume of Gas at Point 1 = 3
T_s = Saturated Temprature = 2

T_sup = ^{x(V_g1 T_s)} / _Vg2
T_sup = ^14(3)(2) / ₄
T_sup = ⁸⁴ / ₄
T_sup = 21

Therefore, the superheated steam temperature is 21.

Calculating the Saturated Temperature when the Dryness Fraction, the Specific Volume of Gas at Point 2, the Specific Volume of Gas at Point 1 and the Superheated Steam Temperature is Given.

T_s = ^{V_g2 T_sup} / _{x Vg1}

Where:

T_s = Saturated Temprature
x = Dryness Fraction
V_g2 = Specific Volume of Gas at Point 2
V_g1 = Specific Volume of Gas at Point 1
T_sup = Superheated Steam Temprature

Let’s solve an example;
Find the saturated temperature when the dryness fraction is 8, the specific volume of gas at point 2 is 4, the specific volume of gas at point 1 is 10 and the superheated steam temperature is 16.

This implies that;

x = Dryness Fraction = 8
V_g2 = Specific Volume of Gas at Point 2 = 4
V_g1 = Specific Volume of Gas at Point 1 = 10
T_sup = Superheated Steam Temprature = 16

T_s = ^{V_g2 T_sup} / _{x Vg1}
T_s = ^(4)(16) / _(8)(10)
T_s = ⁶⁴ / ₈₀
T_s = 0.8

Therefore, the saturated temperature is 0.8

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the dryness fraction at constant volume heating or cooling.

Now, Click on Chemical Reaction Thermodynamics under Materials and Metallurgical

Now, Click on Enthalpy under Chemical Reaction Thermodynamics

Now, Click on Dryness Fraction at Constant Volume Heating or Cooling under Enthalpy

The screenshot below displays the page or activity to enter your values, to get the answer for the dryness fraction at constant volume heating or cooling according to the respective parameter which is the Specific Volume of Gas at Point 2 (V_g2), Specific Volume of Gas at Point 1 (V_g1), Superheated Steam Temprature (T_sup) and Saturated Temprature (T_s).

Now, enter the values appropriately and accordingly for the parameters as required by the Specific Volume of Gas at Point 2 (V_g2) is 4, Specific Volume of Gas at Point 1 (V_g1) is 9, Superheated Steam Temprature (T_sup) is 6 and Saturated Temprature (T_s) is 2.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the dryness fraction at constant volume heating or cooling and presents the formula, workings and steps too.