# Question #0624a

Dec 5, 2017

Heat required$=$ 143.2Kcal

#### Explanation:

The process can be split into 3 steps for simplification:

200 gms of ICE at ${0}^{0} C \textcolor{red}{\Rightarrow}$200 gms of WATER at ${0}^{0} C \textcolor{b l u e}{\Rightarrow}$

200 gms of WATER at ${100}^{0} C \textcolor{g r e e n}{\Rightarrow}$200 gms of STEAM at ${100}^{0} C$

1 . In first step

200 gms of ICE at ${0}^{0} C \textcolor{red}{\Rightarrow}$200 gms of WATER at ${0}^{0} C$

The heat energy required is

$\textcolor{red}{L A T E N T . H E A T . O F . F U S I O N . O F . I C E}$

[ Quantity of heat required to change 1 Kg of a substance from solid state to liguid state at its Melting point}

Latent heat of fusion of ICE$=$80cal/gm

So heat required for 200gm$\Rightarrow$80$\frac{c a l}{g m}$$\times$200gm$\rightarrow$1600cal $=$16Kcal

2.) 200 gms of WATER at ${0}^{0} C \textcolor{b l u e}{\Rightarrow}$200 gms of WATER at ${100}^{0}$

Q$=$mS$\Delta$T {m$\rightarrow$mass:S$\rightarrow$specific heat; T$\rightarrow$Temperature}

SPECIFIC HEAT OF WATER$\rightarrow$1 cal/g-${C}^{0}$

Q$=$200$\cancel{g m}$$\times$1 cal/$\cancel{g m - {C}^{0}}$$\times$(100-0)$\cancel{{C}^{0}}$$\Rightarrow$20Kcal

3.) 200 gms of WATER at ${100}^{0} C \textcolor{b l u e}{\Rightarrow}$200 gms of STEAM at ${100}^{0} C$

Heat energy required is

$\textcolor{b l u e}{L A T E N T . H E A T . O F . V A P O R I Z A T I O N . O F . W A T E R}$}

{ Quantity of heat energy required to change its 1 kg mass from

liquid to vapour state at its boiling point,}

Latent heat of vaporisation of water:

536Kcal/gm$\rightarrow$536cal/gm$\Leftrightarrow$ 540cal/gm

So heat required for vaporisation of 200gm water to steam at ${100}^{0} C$$\Rightarrow$ 536$\frac{c a l}{\cancel{g m}} \times$200$\cancel{g m}$$=$107.2Kcal{108Kcal$\rightarrow$ if you use 540cal/gm}

The amount of heat (in Joules) required to convert 200 grams of ice
to gas at 100 degrees celsius is the sum heat of 3 steps

$\Rightarrow$16Kcal+20Kcal+107.2Kcal$=$ 143.2Kcal{144Kcal$\rightarrow$If you use L.H.V as 540cal/g}