How Do You Determine the Rise in Temperature of a Rock Falling into Water?

In summary, the rock of mass 0.19 kg falls from rest from a height of 15 m into a pail containing 0.37 kg of water, both at the same initial temperature. Using the formula Q=cm(delta T), we can determine the rise in temperature of the rock and water, assuming that the mechanical energy of the rock is converted to heat. By approximating with PE = mgh, we can equate the potential energy of the rock to the total increase in heat energy, which can be calculated using the specific heat capacities of the rock and water.
  • #1
copitlory8
86
0
Thermodynamics

A rock of mass 0.19 kg falls from rest from a height of 15 m into a pail containing 0.37 kg of water. The rock and water have the same initial temperature. The specific heat capacity of the rock is 1885 J/(kg·C°). Ignore the heat absorbed by the pail itself, and determine the rise in the temperature of the rock and water.

I listed by knowns and unknowns. The rock is of mass .19kg and the distance is 15m. The mass of water is .37kg. The Tinitial is the same for both water ad rock. Heat capacity of the rock is 1885.

I have no idea how to solve this except that it involves using the formula Q=cm(delta T)

Please give me a solution. Thanks
 
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  • #2


Assume that the mechanical energy of the rock is converted to heat.

ehild
 
  • #3


so does this mean to use a mechanical energy equation.
 
  • #4


Yes, assume that the mechanical energy of the rock is conserved during the fall. When it splashes into the water, the water is brought into chaotic motion and the energy of this motion is transformed into the energy of the random motion of molecules, that is, heat.
 
  • #5


PE=mgh
KE= .5(m)(v)^2
E=PE+KE (I am not sure if this is the right equation for mechanical energy?)
 
  • #6


copitlory8 said:
PE=mgh
KE= .5(m)(v)^2
E=PE+KE (I am not sure if this is the right equation for mechanical energy?)

You can use E=PE+KE for a certain position of the rock. If it is at rest at height of 15 m, does it have kinetic energy?
When it fall down to the ground what is the potential energy?

ehild
 
  • #7


no kinetic energy
 
  • #8


So what is the mechanical energy of the rock?

ehild
 
  • #9


just potential energy
 
  • #10


copitlory8 said:
just potential energy
how much?

ehild
 
  • #11


now my head really hurts. i have no idea. can i get a detalied step by step solution. this thing is due by 6:00
 
  • #12


copitlory8 said:
A rock of mass 0.19 kg falls from rest from a height of 15 m into a pail containing 0.37 kg of water. The rock and water have the same initial temperature. The specific heat capacity of the rock is 1885 J/(kg·C°). Ignore the heat absorbed by the pail itself, and determine the rise in the temperature of the rock and water.

I listed by knowns and unknowns. The rock is of mass .19kg and the distance is 15m. The mass of water is .37kg. The Tinitial is the same for both water ad rock. Heat capacity of the rock is 1885.

I have no idea how to solve this except that it involves using the formula Q=cm(delta T)

Please give me a solution. Thanks

Since the height of fall is small, we can approximate with PE = mgh

Considering that all PE is converted to KE which subsequently converts to the total increase in heat energy,

PE = Heat(Rock) + Heat (Water
(0.19)(15)(9.81) = (0.19)(1885)(change temp) + 0.37(4200)(change temp)

By switching things around, you should get the answer.
 

FAQ: How Do You Determine the Rise in Temperature of a Rock Falling into Water?

What is the final velocity of the rock when it falls into the pail?

The final velocity of the rock can be calculated using the equation v = √(2gh), where g is the acceleration due to gravity (9.8 m/s^2) and h is the height from which the rock falls. Plugging in the values, we get v = √(2*9.8*15) = 17.15 m/s.

How much potential energy does the rock have at the top of the pail?

The potential energy of the rock at the top of the pail can be calculated using the equation PE = mgh, where m is the mass of the rock (0.19 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height from which the rock falls (15 m). Plugging in the values, we get PE = 0.19*9.8*15 = 27.93 J.

What is the kinetic energy of the rock when it hits the bottom of the pail?

The kinetic energy of the rock at the bottom of the pail can be calculated using the equation KE = 1/2 mv^2, where m is the mass of the rock (0.19 kg) and v is the final velocity of the rock (17.15 m/s). Plugging in the values, we get KE = 1/2*0.19*17.15^2 = 28.97 J.

How much work is done by the rock as it falls into the pail?

The work done by the rock can be calculated by multiplying the force (weight of the rock) by the displacement (height). Since the rock is falling vertically, the force is equal to its weight, which can be calculated using the equation F = mg, where m is the mass of the rock (0.19 kg) and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get F = 0.19*9.8 = 1.862 N. The displacement is 15 m. Therefore, the work done by the rock is 1.862*15 = 27.93 J.

What happens to the energy of the system after the rock falls into the pail?

After the rock falls into the pail, its potential energy is converted into kinetic energy as it accelerates towards the bottom. When it hits the bottom, all of its potential energy is converted into kinetic energy. Some of this kinetic energy is then transferred to the water in the pail, causing it to splash and move. The remaining kinetic energy is converted into heat and sound energy upon impact. Overall, the total energy of the system (rock and pail) remains constant, but it is converted from one form to another.

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