Geophysicists study the rheology of magma to predict volcanic eruption styles. A volcanolo… — ACT

Geophysicists study the rheology of magma to predict volcanic eruption styles. A volcanologist formulated a hypothesis regarding the combined effects of pressure ( $P$ ) and water content ( $W$ ) on the viscosity ( $\eta$ ) of rhyolitic magma at a constant temperature of $1000^\circ\text{C}$ :

*Hypothesis*: Increasing $W$ decreases $\eta$ by disrupting silicate network bonds. However, because higher $P$ compresses the melt and opposes this bond disruption, the viscosity-reducing effect of adding water (defined as the factor by which $\eta$ decreases when $W$ is increased from $0.1\text{ wt}\%$ to $3.0\text{ wt}\%$ ) will become weaker as $P$ increases.

To test this hypothesis, the volcanologist measured the viscosity of rhyolitic magma samples at $1000^\circ\text{C}$ under different combinations of $P$ and $W$ . The results are shown in the table below:

Trial	Pressure ( $P$ , $\text{MPa}$ )	Water content ( $W$ , $\text{wt}\%$ )	Viscosity ( $\eta$ , $\text{Pa}\cdot\text{s}$ )
1	50	0.1	$1.0 \times 10^8$
2	50	1.0	$5.0 \times 10^5$
3	50	3.0	$2.0 \times 10^3$
4	150	0.1	$8.0 \times 10^7$
5	150	1.0	$1.0 \times 10^5$
6	150	3.0	$9.0 \times 10^2$
7	300	0.1	$5.0 \times 10^7$
8	300	1.0	$3.0 \times 10^4$
9	300	3.0	$4.0 \times 10^2$

Which of the following statements best describes how the volcanologist should modify the hypothesis in light of these results?

Modify the hypothesis to state that the viscosity-reducing effect of water becomes stronger as pressure increases, because the factor by which viscosity decreases when water is added increases as pressure increases.Cevap
B
Modify the hypothesis to state that the viscosity-reducing effect of water becomes weaker as pressure increases, because the absolute decrease in viscosity when water is added is smallest at $300\text{ MPa}$ .
C
Retain the hypothesis because at each pressure, increasing the water content from $0.1\text{ wt}\%$ to $3.0\text{ wt}\%$ decreases the magma viscosity.
D
Modify the hypothesis to state that increasing pressure increases magma viscosity, because compaction at higher pressures prevents water from effectively lubricating the silicate network.

Cevap

Modify the hypothesis to state that the viscosity-reducing effect of water becomes stronger as pressure increases, because the factor by which viscosity decreases when water is added increases as pressure increases.

The correct option correctly identifies that the volcanologist's hypothesis must be modified to state that the viscosity-reducing effect of water becomes stronger at higher pressures. The hypothesis defines the effect as the factor by which viscosity decreases when water is increased from

0.1\text{ wt}\%

3.0\text{ wt}\%

. Calculating this factor (viscosity at

0.1\text{ wt}\%

divided by viscosity at

3.0\text{ wt}\%

) yields

50,000

50\text{ MPa}

, approximately

88,889

150\text{ MPa}

, and

125,000

300\text{ MPa}

. Since this factor increases with pressure, the effect becomes stronger, contradicting the hypothesis that it would become weaker.

Adım Adım Çözüm

Identify the definition of the viscosity-reducing effect in the hypothesis.

The effect is defined as the factor (ratio) by which viscosity decreases when water content increases from

0.1\text{ wt}\%

3.0\text{ wt}\%

This sets the criteria for evaluating the strength of the water's effect.

Calculate the reduction factor at each pressure level using the formula:

\text{Factor} = \frac{\eta_{\text{at } 0.1\%}}{\eta_{\text{at } 3.0\%}}

50\text{ MPa}

\frac{1.0 \times 10^8}{2.0 \times 10^3} = 50,000

. At

150\text{ MPa}

\frac{8.0 \times 10^7}{9.0 \times 10^2} \approx 88,889

. At

300\text{ MPa}

\frac{5.0 \times 10^7}{4.0 \times 10^2} = 125,000

This quantifies the strength of the viscosity-reducing effect of water at each pressure.

Compare the calculated factors across different pressures to see if they increase or decrease.

As pressure increases from

50\text{ MPa}

300\text{ MPa}

, the factor of decrease increases from

50,000

125,000

This allows us to determine the trend in the viscosity-reducing effect as pressure increases.

Evaluate the hypothesis against this trend and determine the modification.

The hypothesis predicted the effect would become weaker (factor would decrease), but the data shows it becomes stronger (factor increases). Therefore, the hypothesis must be modified to state the effect becomes stronger as pressure increases.

This directly answers the question.

Anahtar Kavram

Evaluating and modifying a hypothesis based on experimental results by analyzing relative rates of change in a controlled experiment.

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