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Question: The density of ice is x gm/cc and that of water is y gm/cc. What is the change in volume in cc., whe...

The density of ice is x gm/cc and that of water is y gm/cc. What is the change in volume in cc., when m gm of ice melts?
A. m(y−x)m\left( {y - x} \right)
B. (y−x)m\dfrac{{\left( {y - x} \right)}}{m}
C. mxy(x−y)mxy\left( {x - y} \right)
D. m(1y−1x)m\left( {\dfrac{1}{y} - \dfrac{1}{x}} \right)

Explanation

Solution

In this question, density as well as mass of both ice and water is given. Now as we know that even after the change of state, mass of a substance remains the same (unlike weight), by using the formula of Volume and inserting the given values into it, we will be able to calculate the change in volume and hence lead to the solution of our query.

Complete Step-by-Step solution:
When the physical state of water changes, it’s volume, too, gets changed but that is not the case with mass, as mass is a constant property of any given object & doesn’t change with the state of substance. The weight of ice and water may differ when the ice melts into water but the mass will not change.
Hence, Let’s take the mass of both ice and water as m.
Density of ice as x gm/cc and density of water as y gm/cc, where gm stands for gram and cc for cubic centimetre.
Gram per cubic centimetre is the standard unit of density in the CGS system.

mass = volume × density
So, volume of m-g of ice = massdensity\dfrac{{mass}}{{density}}
⇒(mx)\Rightarrow \left( {\dfrac{m}{x}} \right)cc.
So, volume of m-g of water = massdensity\dfrac{{mass}}{{density}}
⇒(my)\Rightarrow \left( {\dfrac{m}{y}} \right)cc.

To calculate the volume difference in both the states, subtract volume of m-g of ice from volume of m-g of water –
⇒(my)−(mx)=m(1y−1x)\Rightarrow \left( {\dfrac{m}{y}} \right) - \left( {\dfrac{m}{x}} \right) = m\left( {\dfrac{1}{y} - \dfrac{1}{x}} \right)
Hence, the correct answer is (D) m(1y−1x)m\left( {\dfrac{1}{y} - \dfrac{1}{x}} \right).

Note: - The volume of ice decreases when it melts into water. Hence, volume of m-g of ice is slightly greater than volume of m-g of water. Therefore, to yield a positive value for the difference in volume, volume of water should be subtracted from volume of ice. This information can be used to easily solve the above query.