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How Do You Calculate Change in Specific Volume?

Published in Thermodynamics 3 mins read

The change in specific volume is calculated by finding the difference between the final specific volume and the initial specific volume. The specific method depends on the information available. Here's a breakdown:

Understanding Specific Volume

Specific volume (ν) is the volume occupied by a unit mass of a substance. It's the reciprocal of density.

Methods to Calculate Change in Specific Volume (Δν)

  1. Direct Calculation Using Volume and Mass:

    If you know the initial volume (V1), final volume (V2), and mass (m) of the substance, you can calculate the change in specific volume as follows:

    • Initial specific volume: ν1 = V1 / m
    • Final specific volume: ν2 = V2 / m
    • Change in specific volume: Δν = ν2 - ν1 = (V2 / m) - (V1 / m) = (V2 - V1) / m

  2. Using Density:

    If you know the initial density (ρ1) and final density (ρ2), you can calculate the change in specific volume as:

    • Initial specific volume: ν1 = 1 / ρ1
    • Final specific volume: ν2 = 1 / ρ2
    • Change in specific volume: Δν = ν2 - ν1 = (1 / ρ2) - (1 / ρ1)

  3. Using the Ideal Gas Law (for Ideal Gases):

    If you are dealing with an ideal gas and know the initial and final states (Pressure, Temperature), you can use the ideal gas law to determine specific volume:

    • Specific volume: ν = RT / P, where:

      • R is the specific gas constant (R = Ru/M, where Ru is the universal gas constant and M is the molar mass)
      • T is the absolute temperature (in Kelvin or Rankine)
      • P is the absolute pressure

    • Initial specific volume: ν1 = R * T1 / P1

    • Final specific volume: ν2 = R * T2 / P2

    • Change in specific volume: Δν = ν2 - ν1 = (R T2 / P2) - (R T1 / P1)

Example

Let's say you have 2 kg of a gas. Initially, its volume is 1 m3, and after some process, its volume becomes 1.5 m3.

  • m = 2 kg
  • V1 = 1 m3
  • V2 = 1.5 m3
  1. Calculate initial specific volume: ν1 = V1 / m = 1 m3 / 2 kg = 0.5 m3/kg
  2. Calculate final specific volume: ν2 = V2 / m = 1.5 m3 / 2 kg = 0.75 m3/kg
  3. Calculate the change in specific volume: Δν = ν2 - ν1 = 0.75 m3/kg - 0.5 m3/kg = 0.25 m3/kg

Therefore, the change in specific volume is 0.25 m3/kg.

Summary

To calculate the change in specific volume, determine the initial and final specific volumes using the appropriate formula based on the available data (volume & mass, density, or ideal gas law parameters), and then subtract the initial specific volume from the final specific volume.

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