密度和比重之间的差异

密度定义为单位体积物质中的质量。密度是一种内在属性，因为它取决于给定材料中原子的内部堆积以及元素或化合物的原子质量。这意味着无论外部条件如何，材料的密度都将保持不变。密度的标准单位是Kg/m ³ 。

在数学上，密度是质量和体积的比值，用希腊字母roh (ρ) 表示。

Density = Mass/Volume

物质的比重是其密度与另一种参考物质的比值。它是一个无单位的数量。比重是一个模棱两可的术语，因为重力与它无关，因此更经常使用术语相对密度。

如果一种物质的比重小于 1，那么它将淹没在参考物质中，如果比重大于 1，那么该物质将漂浮在参考物质中。

对于流体，参考物质通常是水 (10 ³ kg/m ³ )，对于气体，参考物质通常是室温下的空气 (1.2 kg/m ³ )。

Specific gravity = ρ_i/ρ_o 

where, 

ρ_i = density of substance,

ρ_o = density of reference substance.

以下是密度和比重之间的差异表：

	Density	Specific Gravity
1.	It is the relationship between the mass and volume of a substance.	It is the ratio of the density of a substance and a reference substance.
2.	Density is an absolute quantity.	Specific gravity is a relative quantity.
3.	Density = Mass/Volume	Specific gravity = ρi/ρo
4.	Density is unique for material under a given temperature.	Specific gravity for a single substance can vary depending upon the reference substance used.
5.	It’s unit is Kg/m3	It is unit-less.

示例问题

问题1：铜条的尺寸为1.5cm X 1.0cm X 3.0cm，质量为37.5gm。求它的密度。

解决方案：

Density = Mass/Volume, so in order to calculate density we’ll need the volume of the copper bar.

volume = l x b x h

volume = 1.5 x 1.0 x 3.0 

volume = 4.5 cm³

mass =  37.5 gm

=> density = 40/4.5 = 9.99 gm/cm³

问题2：一个固体塑料玩具在完全浸入水中时位移24 cm ³ ，如果它的质量是29gm，求它的密度。

解决方案：

Density = Mass/Volume, volume of the plastic toy will be equal to the volume of the water

that it displaces.

therefore volume = 24 cm³ 

mass = 29gm

=> density = 24/29 = 0.83 gm/cm³  

问题3：一个直径80mm、质量160g的足球落入水中。计算足球的比重并判断它会漂浮还是下沉。

解决方案：

A football is a sphere, so it’s volume is 4/3 * π * r³ 

converting radius from mm to cm and plugging it in the formula we get 

volume of football = 4/3 * π * 4³ = 2144.66 cm³.

mass = 160g

=> density = 160/2144.66 = 0.074 gm/cm³

specific gravity = density of football / density of water

=>specific gravity = 0.074/1 = 0.074

as the specific gravity of football is less than 1 the ball will float on water. 

问题4：比重的单位是什么？

解决方案：

As specific gravity is a ratio of densities, it doesn’t have any units.

问题 5：密度为 1 gm/cm ³的 200 ml 酒精必须加入多少密度为 0.8 gm/cm ³的水才能使其密度达到 0.9 gm/cm ³ ？

解决方案：

weight of 200 ml of alcohol = density * volume

weight of 200 ml of alcohol = 0.8 * 200 = 160 gm

let us assume that adding ‘x’ gram of water will bring specific gravity of alcohol to 0.9.

volume of x gram of water = 1 * x = x ml.

=> final mass of the solution (water + alcohol) = 160 + x 

and final volume of the solution = 200 + x.

density of solution = (160 + x) / (200 + x)

=> (160 + x) / (200 + x) = 0.9

=> 160 + x = 180 + 0.9x

=> 0.1x = 20

=> x = 200

therefore 200 gm of water must be added to 200 ml of alcohol to make the alcohol’s density to 0.9.