# Measuring volume change from change in mass

I want to measure the expansion (by change in volume) of a material in liquid. However the shapes are so complex that I can only measure their mass. Is it possible to compute the volume of the expanded shape by measuring its mass alone?

Given mass $m_0$ at $t_0$ and mass $m_1$ at $t_1$ and the density $\rho_\mathrm m$ of the material and $\rho_\mathrm l$ of the liquid, can I find the volume change of the object from $t_0$ to $t_1$?

One could assume that $(m_0-m_1)/\rho_\mathrm l$ is the correct answer, but I am not sure if this is the right way to go about it?

• Can you measure the volume by displacement, as Archimedes did? [Do not run through the streets shouting 'Eureka!", though.] – DrMoishe Pippik Jul 11 '16 at 5:13
• I assume that "from t0 to t1" part of the question means that the temperature is changing. – MaxW Feb 14 '17 at 2:13
• Is there a way to know the starting volume? Is the material compact and easy to be handled? – Alchimista Jul 14 '17 at 20:30

## 2 Answers

You can't compute the volume of a solid from the mass alone.

You can measure the specific gravity as a function of the temperature of the liquid. You'd need to know how the density of the liquid changes with temperature to convert the specific gravity data at each temperature to actual density value which could then be used to calculate the effective volume of the solid at each temperate.

The standard way would be to measure the weight of material in air and in a liquid. This would give you the density of the material from Archimedes law.

However, Archimedes worked with gold/silver which doesn't react with water. You need to know density before and after the experiment so you need to weight dry material in air and liquid, let it soak in water and then measure its weight in air and liquid again. You should be able to weight your material in air and, say, ether (non reactive, known density, evaporates fast), dry your material, soak it in water, weight it in water and then weight it in dry air. Depending on the nature of the material it might or might not work. Zeolite will interact with either and alter the results.

• This is only half an answer. How do you propose to handle the temperature variation? – MaxW Nov 15 '16 at 22:41