Work in a Constant Volume

[Linette Choi 3L]

Hello! I know that work is equal to 0 when volume is constant but can someone explain why we can assume that?

[Sofia Azmat 1I]

You're describing an isochoric process or as you stated, a constant volume process. The formula for work is w=PΔV, and if there is a constant volume, that means there is ZERO change in volume. Because ΔV = 0 , any P value that you multiply it by is going to give you 0 for work. w=P(0) will always mean work equals zero.

Another way to think about work is graphically, with your x-axis being V and y-axis being pressure and work equaling the area under the curve. Since volume remains constant, there is no area under the curve, therefore giving you zero. If you look up a constant volume graph vs a constant pressure graph, you can see this visually.

[Simrah_Ahmed1J]

Mathematically, it is from the w=PΔV equation. But the way to think about it, in general, is that because that no work of expansion is done (like when it comes to solids and liquids), the volume of the reactants and products is equal. That's why there is no change in volume when there is no work!

[Julianna_flores3E]

At a constant volume, work can be defined as force x distance since there is no change in volume (distance) then the equation if force x 0 = 0 therefore, work =0.

[Hannah_Kim_1I]

Since the equation for work of expansion in w=-PdeltaV, if the volume is constant, it makes delta v 0 since there is no change in volume. Since anything multiplied by 0 is 0, we can assume work will be 0.

[LovepreetSran_3H]

In the equation w= -PdeltaV if the volume is constant then the change in volume is zero. Therefore -P(0) = 0 showing why the work is 0 at constant volume.

[Taylor K 2D]

Conceptually: when there is no change in volume, there is no expansion or compression, and therefor no work being done. Mathematically: for the equation w = -P∆V, and so if the change in volume is zero, then the work done will also be zero. for the equation w = -nRT ln V2/V1, the natural log of V2/V1 would become ln(1), which is zero, making work also equal to zero.

[Uyen Trinh 3C]

You're describing an isochoric process or as you stated, a constant volume process. The formula for work is w=PΔV, and if there is a constant volume, that means there is ZERO change in volume. Because ΔV = 0 , any P value that you multiply it by is going to give you 0 for work. w=P(0) will always mean work equals zero.

Another way to think about work is graphically, with your x-axis being V and y-axis being pressure and work equaling the area under the curve. Since volume remains constant, there is no area under the curve, therefore giving you zero. If you look up a constant volume graph vs a constant pressure graph, you can see this visually.

Sofia explains this really well. I need to understand what it means literally for the volume to not change in the real world and then apply it to the formulas given.

[Alexis Sanft 1E]

Does this have anything to do with neutralization of a reaction, and if not what exactly is neutralization of a reaction and how do we know what we are solving for in this type of reaction?

[Joshua_Chan_3K]

We use the equation work = P times delta V so obviously if delta V is 0 then work = 0. I remember it using the equation I learned in physics which comes from the definition of work as distance times force. Work is dependent on a distance being acted upon so if there is no movement (constant volume) then work has to equal 0.

[Pratika Nagpal]

There are 2 ways to think about this, either conceptually or mathematically - the formula for work is PdeltaV and no change in volume delta v =0 , and therefore w=0. Another way to think about it since there is no expansion, there is no work done by the system. and therefore work is 0

[Pratika Nagpal]

I don't exactly know how to relate this to neutralization of a reaction, but a neutralisation reaction is basically the reaction between an acid and a base to form a soluble salt and water. Neturalisation reactions are usually exothermic due to the formation of the bond between hydrogen and oxygen to yield liquid water. Since the reaction is exothermic, the work is being done by the system, work is negative.

[Sondia Luong 1C]

Since the equation for work is -P∆V, if volume is constant, that means ∆V = 0. Since ∆V equals 0, then work will also equal 0!

[Aanya Tanti 3C]

In an irreversible reaction, w= -P x delta V. Thus if there is no change in volume, w must also be 0.