an ice block at 0 degree celcius is dropped from height 'h' above the ground. what should be the value of 'h' so that it just melts completely by the time it reaches the bottom assuming the loss of whole gravitational potential energy is used as heat by the ice ? (given: Lf = 80 cal/gm )
80 cal = 335 joules
so Lf = 335 Joules / .001 kg - 335,000 Joules/kg
potential energy = m g h
m g h = m (335,000)
9.81 h = 335,000
h = 34,149 meters
To calculate the value of 'h' at which the ice block just melts completely by the time it reaches the bottom, we need to consider the energy balance between the loss of gravitational potential energy and the heat required to melt the ice.
First, let's calculate the energy required to melt the ice completely. The heat required to melt one gram of ice is given as latent heat of fusion (Lf) = 80 cal/gm.
Next, we need to calculate the gravitational potential energy (PE) of the ice block. The formula for gravitational potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
Since the ice block is dropped from rest, it has an initial gravitational potential energy of mgh at height h.
Now, we'll equate the gravitational potential energy with the heat required to melt the ice:
mgh = Lf * m
Here, the mass (m) of the ice cancels out, simplifying the equation to:
gh = Lf
Now, substitute the given value of Lf = 80 cal/gm and convert it into joules using the conversion factor 1 cal = 4.18 J:
gh = 80 cal/gm * 4.18 J/cal
Simplifying further:
gh = 334.4 J/gm
Finally, divide both sides of the equation by g to solve for h:
h = 334.4 J/gm / 9.8 m/s^2
h ≈ 34.14 meters
Therefore, the value of 'h' should be approximately 34.14 meters for the ice block to just melt completely by the time it reaches the ground.