# Finding Minimum Work to Compress Water

• megisacat
In summary, the question is asking for the minimum work required to compress 1 kg of water isothermally from p1=1 bar, T1=120C to a volume that is 1/3 the original volume. To solve this, the first step is to determine the phase of the water, which in this case is superheated vapor. Then, using the properties (v,u,h,s) for that temperature and pressure from the superheated table, the specific volume at 1 can be used to find the specific volume at 2. From there, the state at 2 can be determined and the quality can be found using tables, which allows for the calculation of u, h, and s. The

## Homework Statement

Find the minimum work to compress 1 kg of water isothermally from p1=1 bar, T1=120C to a volume that is 1/3 the original volume.

## Homework Equations

Energy balance Q-W=U+KE+PE

## The Attempt at a Solution

So first I found the phase of the water (p<psat for that temp so superheated vapor)
I found the properties (v,u,h,s) for that temperature and pressure in the superheated table.
I can use the specific volume at 1 to find the specific volume at 2 because mass stays constant (closed system) and it's just 1/3 v1. I used that specific volume to determine the state at 2 (in between vf and vg so it's in the saturated liquid vapor phase). I found the quality using tables so I can calculate u, h, s.

I'm mostly confused about the energy balance: I'm pretty sure I can neglect KE and PE. Is there a Q value though? When I went over this problem with the professor he hinted at using TdS equations (Gibbs?) for finding the heat. The Tds equation that I know is Tds=du+Pdv (which is similar to the energy balance since Pdv is the work and du is the the change in internal energy). Do I do W=du+Tds?

Or maybe it is okay to just assume no heat transfer and do W=U and then do m(u2-u1). I'm mostly confused about when you can assume things when doing energy balance.

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You know that the temperature is constant right, and for minimum work, Q = ∫TdS, so Q=TΔS. Just get the Δs from your tables and calculate Q.

## What is "Finding Minimum Work to Compress Water"?

"Finding Minimum Work to Compress Water" is a scientific concept that involves determining the minimum amount of energy or work required to compress a given volume of water. This information is important in various fields such as engineering, physics, and environmental science.

## What factors affect the minimum work required to compress water?

The minimum work required to compress water is affected by several factors, including the initial volume of water, the final compressed volume desired, the pressure applied, and the temperature of the water. Other factors such as the type of container used and the presence of impurities can also have an impact on the minimum work required.

## How is the minimum work to compress water calculated?

The minimum work required to compress water is calculated using the formula W = P(V2-V1), where W is the work in joules, P is the pressure in pascals, V2 is the final compressed volume, and V1 is the initial volume of water. This formula is derived from the first law of thermodynamics, which states that the change in energy of a system is equal to the work done on the system.

## Why is it important to determine the minimum work to compress water?

Knowing the minimum work required to compress water can have practical applications in various industries. For example, in hydraulic systems, engineers need to know the minimum work required to compress water in order to design efficient and effective systems. In addition, this information can also help in understanding the behavior of water under different conditions and can aid in the development of new technologies and materials.

## Are there any challenges or limitations in finding the minimum work to compress water?

One of the main challenges in finding the minimum work to compress water is the complexity of the system. Water is a highly dynamic and complex substance, and its behavior can be affected by various factors such as temperature, pressure, and impurities. Additionally, the calculations for minimum work can become more complicated when dealing with non-ideal conditions or when considering the effects of external forces such as gravity.