# When $1g$ of water at $100{}^\circ C$ gets converted into steam at the same temperature, the change in volume is approximately:

A.$1$$cc$

B.$1000$$cc$

C.$1500$$cc$

D.$1670$$cc$

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**Hint:**Before talking about the answer, we should know what steam is. Steam is defined as a water which is in gas form. It is formed due to evaporation. Here, we are going to find the change in the volume with the help of density formula.

**Formula used:**$m=\delta V$

where $m$ is the mass of water, $\delta $ is the density of water and $V$ is the volume of water.

**Complete step by step answer:**

When water is heated, it will start evaporating, that means it starts getting converted into water vapour and expands. At $100{}^\circ C$ , the water gets evaporated and converted into steam, which is an invisible gas.

Here, it is given that $1g$ of water at $100{}^\circ C$ gets converted into steam at the same temperature.

And as we know, density of water, $\delta =1000kg/{{m}^{3}}$

$\Rightarrow 1g/c{{m}^{3}}$

And density of steam, $\delta =0.6kg/{{m}^{3}}$

$\Rightarrow 0.0006g/c{{m}^{3}}$

Here, mass of water $(m)$ is $1g$

$m=\delta V$

Substituting the values we have, in the above formula, we get

$V=\dfrac{m}{\delta }$

$V=\dfrac{1}{1}=1$

$V$ denotes as the volume of water

Volume of water is $1cc$ .

Volume of the steam,

${V}'=\dfrac{m}{\rho }$

$V'=\dfrac{1}{0.0006}=1666.7cc\approx 1667cc$

$V'$ denotes as the volume of steam

Here, the density of steam is used.

Therefore, the change in volume,

$

\Delta V={V}'-V \\

\Delta V=1667-1=1666cc \\

$

which is close to $1670$$cc$

**So, the correct option is (D), that is, $1670$$cc$ .**

**Additional Information:**

Density is defined as mass per unit volume. For a pure substance, the density is equal to its mass concentration. The density varies with pressure and temperature. The reciprocal of density of a compound is known as specific volume.

Volume is defined as the quantity of three-dimensional space which is occupied by a liquid, solid or a gas. Units that are used to express volume are litres, milliliters, cubic meters.

**Note:**

Make sure to convert $kg/{{m}^{3}}$ to $g/c{{m}^{3}}$. The volume of water and steam is calculated in $cm$ .

The mass of one $cc$ of water at $3.98{}^\circ C$ is nearly equal to one gram.