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小李同学在测量某种液体的密度时，进行了如下实验步骤: (1) 先用天平称出空烧杯的质量

m_{0}

; （2）在烧杯内盛上部分纯水，在水位线处做好标记，并...

Mar 19, 2024

小李同学在测量某种液体的密度时，进行了如下实验步骤: (1) 先用天平称出空烧杯的质量

m_{0}

; （2）在烧杯内盛上部分纯水，在水位线处做好标记，并称出总质量

m_{1}

; (3) 倒出水，擦干烧杯后换上待测液体，使液面到刚才的标记处，再称出总质量

m_{2}

则待测液体的密度为

(

水的密度用

\rho

快表示) （） A.

\rho_{\text {液 }}=\frac{m_{2}-m_{0}}{m_{2}} \cdot \rho_{\text {水 }}

\rho_{\text {液 }}=\frac{m_{2}-m_{0}}{m_{1}-m_{0}} \cdot \rho_{\text {水 }}

\rho_{\text {液 }}=\frac{m_{1}-m_{0}}{m_{2}-m_{0}} \cdot \rho_{\text {水 }}

\rho_{\text {液 }}=\frac{m_{1}-m_{0}}{m_{1}} \cdot \rho_{\text {水 }}

Solution

Identify the mass of the water and the liquid. The mass of the water is

m_{1} - m_{0}

and the mass of the liquid is

m_{2} - m_{0}

Calculate the volume of the water. Since the liquid reaches the same level as the water did, they have the same volume. The volume of the water, using its density

\rho_{\text{水}}

, is

V = \frac{m_{1} - m_{0}}{\rho_{\text{水}}}

Determine the density of the liquid. The density of the liquid is its mass divided by its volume, which is

\rho_{\text{液}} = \frac{m_{2} - m_{0}}{V}

. Substituting the volume from step b, we get

\rho_{\text{液}} = \frac{m_{2} - m_{0}}{\frac{m_{1} - m_{0}}{\rho_{\text{水}}}}

Simplify the expression for the density of the liquid to find the correct answer.

\rho_{\text{液}} = \frac{m_{2} - m_{0}}{m_{1} - m_{0}} \cdot \rho_{\text{水}}

Key Concept

Density and its calculation: Density is mass per unit volume. The density of a substance can be found by dividing its mass by its volume.

Explanation

The density of the liquid is calculated by comparing it to the known density of water and the masses measured during the experiment. The correct formula accounts for the mass of the liquid and the volume it occupies, which is the same as the volume of water that was initially measured.