Thermodynamics : Doubt in First Law I just started my study of thermodynamics. I am having problem in uderstanding a concept.
Suppose I drop an ice-cube and a rock of cube shape. Which one will reach the ground first? I know ratio of Work to Heat equals Joules Constant. Therefore any change in potential energy will result in heat which in return will melt ice cube thus mass is changing. Will internal energy of ice cube change till it reaches the ground? If mass of ice cube is changing what will be the ratio of kinectic energy of ice cube to that of rock.
 A: Your initial assumption is wrong because the ice cube won't melt, or at least not just because it is dropped.
In the Joule experiment work was being converted to heat, however when you drop an ice cube the work done by the gravitational force is converted to kinetic energy not heat. So the temperature of the ice cube doesn't change but its velocity does.
There are a couple of other points we should mention for completeness. Firstly even if the ice cube did melt that wouldn't change its mass since the mass of the water would be the same as the mass of the ice. Secondly even if the mass did change that wouldn't change the rate of fall because the gravitational acceleration is independent of mass.
A: In your assessment of the first law of thermodynamics, you omitted certain terms in the equation that can sometimes be important.  The more complete form of the first law should read $$\Delta U+\Delta (KE)+\Delta (PE)=Q-W$$In your ice cube example, $$\Delta (KE)+\Delta(PE)=0$$So, if the ice cube doesn't exchange significant heat with its surroundings or do significant work on its surroundings while it is falling, $$\Delta U=0$$This means that no ice melts and, even if it was initially below the freezing point, there is no temperature change.
A: The falling process can be quite complex when we come to answer your with one word: stone or water. 
When an object falls, it will be subjected to the following two forces: gravity force and air drag force. If the air drag force can be ignored, the gravity force acts on the object converting the potential energy to a kinetic energy. The answer can easily be that they reach the ground at the same time.  
When there is viscous force, the object shape and its surface viscous force play an important role (e.g. a feature vs. a stone of the same mass). The viscous force is a function of velocity. If they have the same shape, then they reaches the ground at the same time.  
Viscous force does work that converts kinetic energy to heat. This heat will heat up air in vicinity and ice. It can melt the ice cube. The water can change shape easily. With the shape change, the ice will have less drag and reach the ground first.
Viscous force can also shear off some of the water, whereas it would not tear off any material of the stone. This will make the ice smaller and less drag. Ice will hit the ground first. 
The ice may completely evaporate before it reaches ground. In this case, a rock will hit the ground first. 
Now, back to the first law, there are components of potential energy, kinetic energy and internal energy. But there is also an important component: work. Nothing can be ignored and all stone should be turned.
