A 10-kg iron ball is dropped onto a pavement from a height

Question

1. The quantity of heat Q that changes the temperature ΔT of a mass m of a substance is given by Q = cmΔT, where c is the specific heat capacity of the substance. For example, for H₂O, c = 1 cal/g°C. And for a change of phase, the quantity of heat Q that changes the phase of a mass m is Q = mL, where L is the heat of fusion or heat of vaporiza­tion of the substance. For example, for H₂O, the heat of fusion is 80 cal/g (or 80 kcal/kg) and the heat of vaporiza­tion is 540 cal/g (or 540 kcal/kg). Use these relationships to determine the number of calories to change (a) 1 kg of 0°C ice to 0°C ice water, (b) 1 kg of 0°C ice water to 1 kg of 100°C boiling water, (c) 1 kg of 100°C boiling water to 1 kg of 100°C steam, and (d) 1 kg of 0°C ice to 1 kg of 100°C steam.

2. The specific heat capacity of ice is about 0.5 cal/CC. Sup­posing that it remains at that value all the way to absolute zero, calculate the number of calories it would take to change a 1-g ice cube at absolute zero (-273°C) to 1 g of boiling water. How does this number of calories compare with the number of calories required to change the same gram of 100°C boiling water to 100°C steam?

3. Find the mass of 0°C ice that 10 g of 100°C steam will completely melt.

4. Consider 50 g of hot water at 80°C poured into a cavity in a very large block of ice at 0°C. What will be the final temperature of the water in the cavity? Show that 50 g of ice must melt in order to cool the hot water down to this temperature.

5. A 50-g chunk of 80°C iron is dropped into a cavity in a very large block of ice at 0°C. Show that 5.5 g of ice will melt. (The specific heat capacity of iron is 0.11 cal/g°C.)

6. If you drop a piece of ice on a hard surface, the energy of impact will melt some of the ice. The higher it drops, the more ice will melt upon impact. Show that to completely melt a block of ice that falls without air drag, it should ideally be dropped from a height of 34 km. [Hint• Equate the joules of gravitational potential energy to the product of the mass of ice and its heat of fusion (in SI units, 335,000 J/kg). Do you see why the answer doesn't depend on mass?]

7. A 10-kg iron ball is dropped onto a pavement from a height of 100 m. If half of the heat generated goes into warming the ball, find the temperature increase of the ball. (In SI units, the specific heat capacity of iron is 450 J/kg°C.) 'Why is the answer the same for a ball of any mass?

8. The heat of vaporization of ethyl alcohol is about 200 cal/g. If 2 kg of this fluid were allowed to vaporize in a refrigerator, show that 5 kg of ice would be formed from 0°C water.

Answer 1

Answer the following questions of mechanics problem by solving all the parts by applying the appropriate concepts and theories of mechanics. Q1. Determine the mass of 0°C ice which 10 g of 100°C steam will totally melt. Q2. Take 50 g of hot water at 80°C poured to a cavity in a very big block of ice at 0°C. Determine the final temperature of the water in cavity? Explain that 50 g of ice should melt in order to cool the hot water down to this temperature. Q3. A 50 g chunk of 80°C iron is dropped to a cavity in a very big block of ice at 0°C. Illustrate that 5.5 g of ice will melt. Q4. A 10 kg iron ball is dropped to a pavement from a height of 100 m. If half of heat produced goes to warming the ball, determine the temperature rise of the ball.