Thursday, January 28, 2016

Ultimate guide to solve all the "Ice cube melting in Water" questions

You must have read some questions based on "effects of an Ice cube on the water levels", in your SSC, Railway NTPC, Railway JE SSE or any other examination where physics is asked in GK section. We will discuss here the basic theory of "Melting ice and its effects on water levels".

First let's understand two Archimedes' Principles:

1. Any floating object displaces a volume of water equal in weight to the object's MASS.

2. Any submerged object displaces a volume of water equal to the object's VOLUME.

Also, recall formula of density = Mass / Volume.

Now let's take the first problem. If we have placed an ice cube in a glass of water, and the cup is full of water up to the brim, then as the ice melts what will happen to the water level? will water overflow from the cup?

Based on the first principle, an ice cube is floating and it has displaced an amount of water which has similar mass ( or weight) as of mass of ice cube. (Read this twice if needed)
So let's say the ice cube is of  25 gram then 25 gram of water has been moved by an ice cube. ( or there will be space for 25 gram of water in the glass if we remove the ice!!!!)

If you have understood the above properly then let's see another interesting property of water and ice. Water is one of the very few materials that have a lesser density in its solid form. Did you get the last sentence? Recall your experience with refrigerator, we fill the ice tray (or some other pot ) full of water to the brim level, and when we take out the ice, the ice will come slightly over the brim. This means that while we convert water to ice, the volume increases. (to check this phenomenon, take some metallic pot with a smaller opening and fill it full and check the results. make sure to fill it fully after putting in the refrigerator).

Ice has a density of 0.92 grams /cm3 while water has 1 grams/cm3. Let's get back to the question, what will happen to the water level? The answer is the water level will get unchanged because when the ice melts its density increases, and the melted water volume is exactly equal to the amount of water displaced by ice.


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