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Sagot :
To determine the validity of Nathan's hypothesis and where it might lead to further investigations, we need to analyze the data presented in the table. Nathan hypothesized that as the temperature of liquid water increases, the density would decrease. Let's examine the data step by step.
The table shows densities of water at different temperatures:
- At [tex]\( 0.0^\circ C \)[/tex], the density is [tex]\( 0.99981 \)[/tex] g/cm³
- At [tex]\( 1.0^\circ C \)[/tex], the density is [tex]\( 0.999900 \)[/tex] g/cm³
- At [tex]\( 2.0^\circ C \)[/tex], the density is [tex]\( 0.999941 \)[/tex] g/cm³
- At [tex]\( 3.0^\circ C \)[/tex], the density is [tex]\( 0.999965 \)[/tex] g/cm³
- At [tex]\( 4.0^\circ C \)[/tex], the density is [tex]\( 0.999973 \)[/tex] g/cm³
- At [tex]\( 5.0^\circ C \)[/tex], the density is [tex]\( 0.999965 \)[/tex] g/cm³
- At [tex]\( 6.0^\circ C \)[/tex], the density is [tex]\( 0.999941 \)[/tex] g/cm³
We observe the following trends in density as temperature increases:
- From [tex]\( 0.0^\circ C \)[/tex] to [tex]\( 1.0^\circ C \)[/tex]: density increases (0.99981 to 0.999900)
- From [tex]\( 1.0^\circ C \)[/tex] to [tex]\( 2.0^\circ C \)[/tex]: density increases (0.999900 to 0.999941)
- From [tex]\( 2.0^\circ C \)[/tex] to [tex]\( 3.0^\circ C \)[/tex]: density increases (0.999941 to 0.999965)
- From [tex]\( 3.0^\circ C \)[/tex] to [tex]\( 4.0^\circ C \)[/tex]: density increases (0.999965 to 0.999973)
- From [tex]\( 4.0^\circ C \)[/tex] to [tex]\( 5.0^\circ C \)[/tex]: density decreases (0.999973 to 0.999965)
- From [tex]\( 5.0^\circ C \)[/tex] to [tex]\( 6.0^\circ C \)[/tex]: density decreases (0.999965 to 0.999941)
From this analysis, we see that the density actually increases from [tex]\( 0.0^\circ C \)[/tex] to [tex]\( 4.0^\circ C \)[/tex] and then decreases from [tex]\( 4.0^\circ C \)[/tex] to [tex]\( 6.0^\circ C \)[/tex]. This contradicts Nathan's hypothesis that an increase in temperature would lead to a consistent decrease in density.
Since the data reveal that the density of water is greatest at [tex]\( 4^\circ C \)[/tex], it indicates a unique property of water. This is a point where further investigation is needed.
Based on these observations, the most suitable conclusion is:
- The data do not support his hypothesis, so he should investigate why the density is greatest at [tex]\( 4^\circ C \)[/tex].
This choice is appropriate because the data show that the density increase occurs up to [tex]\( 4^\circ C \)[/tex], contradicting the hypothesis. Nathan needs to explore the unique behavior of water at this specific temperature.
The table shows densities of water at different temperatures:
- At [tex]\( 0.0^\circ C \)[/tex], the density is [tex]\( 0.99981 \)[/tex] g/cm³
- At [tex]\( 1.0^\circ C \)[/tex], the density is [tex]\( 0.999900 \)[/tex] g/cm³
- At [tex]\( 2.0^\circ C \)[/tex], the density is [tex]\( 0.999941 \)[/tex] g/cm³
- At [tex]\( 3.0^\circ C \)[/tex], the density is [tex]\( 0.999965 \)[/tex] g/cm³
- At [tex]\( 4.0^\circ C \)[/tex], the density is [tex]\( 0.999973 \)[/tex] g/cm³
- At [tex]\( 5.0^\circ C \)[/tex], the density is [tex]\( 0.999965 \)[/tex] g/cm³
- At [tex]\( 6.0^\circ C \)[/tex], the density is [tex]\( 0.999941 \)[/tex] g/cm³
We observe the following trends in density as temperature increases:
- From [tex]\( 0.0^\circ C \)[/tex] to [tex]\( 1.0^\circ C \)[/tex]: density increases (0.99981 to 0.999900)
- From [tex]\( 1.0^\circ C \)[/tex] to [tex]\( 2.0^\circ C \)[/tex]: density increases (0.999900 to 0.999941)
- From [tex]\( 2.0^\circ C \)[/tex] to [tex]\( 3.0^\circ C \)[/tex]: density increases (0.999941 to 0.999965)
- From [tex]\( 3.0^\circ C \)[/tex] to [tex]\( 4.0^\circ C \)[/tex]: density increases (0.999965 to 0.999973)
- From [tex]\( 4.0^\circ C \)[/tex] to [tex]\( 5.0^\circ C \)[/tex]: density decreases (0.999973 to 0.999965)
- From [tex]\( 5.0^\circ C \)[/tex] to [tex]\( 6.0^\circ C \)[/tex]: density decreases (0.999965 to 0.999941)
From this analysis, we see that the density actually increases from [tex]\( 0.0^\circ C \)[/tex] to [tex]\( 4.0^\circ C \)[/tex] and then decreases from [tex]\( 4.0^\circ C \)[/tex] to [tex]\( 6.0^\circ C \)[/tex]. This contradicts Nathan's hypothesis that an increase in temperature would lead to a consistent decrease in density.
Since the data reveal that the density of water is greatest at [tex]\( 4^\circ C \)[/tex], it indicates a unique property of water. This is a point where further investigation is needed.
Based on these observations, the most suitable conclusion is:
- The data do not support his hypothesis, so he should investigate why the density is greatest at [tex]\( 4^\circ C \)[/tex].
This choice is appropriate because the data show that the density increase occurs up to [tex]\( 4^\circ C \)[/tex], contradicting the hypothesis. Nathan needs to explore the unique behavior of water at this specific temperature.
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