# Why does this question make this simplifying assumption?

• laser
laser
Homework Statement
See description
Relevant Equations
A = Q/It, where A is area, Q is heat, I is intensity, t is time

The question says to "neglect the change of volume of the water". This confuses me. Why do we neglect the change of the water's volume? Let's say we didn't. A = Q/It, where A is area, Q is heat, I is intensity, t is time. Q = mc(deltatheta), mass is constant, specific heat is constant (as mass is constant) and change in temperature is constant. I and t are also constant.

The change of volume of water would change the density of water, yes, but the mass will remain constant.

Why does the question say to neglect the change of volume of the water here?

laser said:
##\dots## but the mass will remain constant.
Does the volume of the container holding the water expand at the same rate as the water?

kuruman said:
Does the volume of the container holding the water expand at the same rate as the water?
Oh, what you are saying is that since the volume is expanding, the area will also expand?

That's not what I'm saying although it is true. You have 200 litres of water in a 200-litre container. Say the heated water expands from 200 litres to 205 litres. For the mass to stay the same, the volume of the container must also expand to at least 205 litres. If it doesn't and there is no safety valve to let water out, the container will burst from the pressure because water is incompressible.

kuruman said:
That's not what I'm saying although it is true. You have 200 litres of water in a 200-litre container. Say the heated water expands from 200 litres to 205 litres. For the mass to stay the same, the volume of the container must also expand to at least 205 litres. If it doesn't and there is no safety valve to let water out, the container will burst from the pressure because water is incompressible.
Ah I see. Let's assume that the volume of the container also expands. Why do we have to assume that the water doesn't expand then?

Are you doing work on the water to raise its temperature, or to decrease its density (since the mass is unchanged but the volume has increased)?

laser said:
Ah I see. Let's assume that the volume of the container also expands. Why do we have to assume that the water doesn't expand then?
The water and the container expand with different expansion coefficients. For example, aluminium has a volume expansion coefficient that is about 1/3 that of water. The author of the problem does not want you to get tangled up with expansion calculations for a mere [4 marks], hence the generous suggestion to "neglect the change of the volume of the water here." That would keep the original mass of the water the same and the calculation simple.

PeroK and laser
laser said:
Why does the question say to neglect the change of volume of the water here?
From the supplied data, we can see that the final answer needs a precision of only 2 significant figures.

Note that the volume expansion coefficient of water is ~0.0002 /ºC. So for a 20ºC rise, the volume would increase by ~0.4%. So it hardly matters here.

I'd guess that the very considerate author of the question didn’t want students wasting their time worrying about this small variation. (Though based on my past experience, very few would have!)

(To find the mass of water,you could use the density at the mid-temperature (30ºC). But it hardly matters in this context.)

PeroK
laser said:
Why does the question say to neglect the change of volume of the water here?
The volume of a fixed mass of water increases with temperature. We have 200 litres of water being raised from 20 degrees to 40 degrees, which will entail an increase in volume. The assumption may be there to fend off those of an excessively pedantic disposition, who might otherwise be scornful of the problem statement.

SammyS and Steve4Physics

## Why does this question make this simplifying assumption?

Simplifying assumptions are often made to reduce the complexity of a problem, making it more manageable and easier to solve. By focusing on the most critical factors and ignoring less significant ones, we can develop a clearer understanding of the core dynamics at play.

## How do simplifying assumptions help in scientific modeling?

Simplifying assumptions help in scientific modeling by reducing the number of variables and interactions that need to be considered. This allows for the creation of models that are easier to analyze and interpret, providing insights that might be obscured in a more complex model.

## What are the risks of making simplifying assumptions?

The primary risk of making simplifying assumptions is that they can lead to oversimplification, potentially ignoring important factors that could influence the outcome. This can result in models or conclusions that are not fully accurate or applicable to real-world scenarios.

## Can simplifying assumptions be justified in all cases?

Simplifying assumptions can be justified when they do not significantly alter the outcome or understanding of a problem. However, it is crucial to evaluate each assumption's impact and ensure that it does not compromise the validity of the results. Transparent documentation of these assumptions is also essential.

## How do you determine which assumptions to simplify in a scientific question?

Determining which assumptions to simplify involves identifying the key variables that have the most significant impact on the problem. This often requires a combination of domain knowledge, preliminary analysis, and sometimes sensitivity analysis to understand how different factors influence the outcomes. The goal is to retain the assumptions that are most critical to the problem while simplifying less impactful ones.

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