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学了密度知识后，小明利用电子秤和量杯测量液体的密度，测出液体和量杯的总质量及液体的体积，得到表格中几组数据，下列说法正确的是（　　）实验次数 ...

Mar 19, 2024

学了密度知识后，小明利用电子秤和量杯测量液体的密度，测出液体和量杯的总质量及液体的体积，得到表格中几组数据，下列说法正确的是（　　）实验次数 1 2 3 液体体积V/cm³ 20 50 80 液体、量杯总质量m/g 30 60 84 A．量杯质量是20g B．该液体的体积为40cm³时，则总质量为52g C．该液体密度为lg/cm³ D．该液体的密度是0.8g/cm³学了密度知识后，小明利用电子秤和量杯测量液体的密度，测出液体和量杯的总质量及液体的体积，得到表格中几组数据，下列说法正确的是（　　）实验次数 1 2 3 液体体积V/cm³ 20 50 80 液体、量杯总质量m/g 30 60 84 A．量杯质量是20g B．该液体的体积为40cm³时，则总质量为52g C．该液体密度为lg/cm³ D．该液体的密度是0.8g/cm³

Solution

Calculate the mass of the cup by comparing the total mass for different volumes of liquid

For the first experiment, the total mass (liquid + cup) is 30g for 20cm³ of liquid

For the second experiment, the total mass (liquid + cup) is 60g for 50cm³ of liquid

The increase in mass from the first to the second experiment is 30g (60g - 30g), and the increase in volume is 30cm³ (50cm³ - 20cm³)

The mass of the liquid alone for the increased volume is 30g, so the density of the liquid is

\frac{30g}{30cm³} = 1g/cm³

The mass of the cup can be found by subtracting the mass of the liquid from the total mass in any experiment. Using the first experiment: mass of the cup = total mass - (density * volume) = 30g - (1g/cm³ * 20cm³) = 10g

The correct statement about the mass of the cup is not A, since the mass of the cup is 10g, not 20g

To find the total mass when the volume of the liquid is 40cm³, we use the density of the liquid (1g/cm³) to find the mass of the liquid, which is 40g. Adding the mass of the cup (10g), the total mass is 50g, not 52g, so statement B is incorrect

Statement C is correct because we calculated the density to be 1g/cm³

Statement D is incorrect because the density is not 0.8g/cm³, it is 1g/cm³

Key Concept

Density is a physical property of a material defined as its mass per unit volume. The formula for density is

\rho = \frac{m}{V}

where

\rho

is the density,

m

is the mass, and

V

is the volume.

Explanation

The density of the liquid was found to be 1g/cm³ by comparing the increase in mass to the increase in volume between experiments. This value was then used to determine the mass of the cup and to evaluate the correctness of the given statements.