# Thermodynamics Problem - the lake :P

• Planck const
In summary, the conversation revolves around a problem involving a lump of ice falling into a lake with a temperature of 0 degrees Celsius. The question is to determine the height from which the lump fell. The conversation includes equations and calculations, with the final answer given in the book being 171 meters. The conversation also includes a discussion on unit conversions to ensure accurate calculations.
Planck const
Hi.. looks like simple problem but the result i got is unreasonable.

## Homework Statement

There is lump of ice, that falling down into a lake that his temperature is 0 celsius degrees.

K of the lump getting melt ( = M that melt/M )

What is the height that from him, the lump fell ?

Ep = mgy

Q = mc(Delta t)

Q = mL

## The Attempt at a Solution

mgy = m*k*(L + t of melting)
(c of the water that melt = 1)
t of melting of water = 0

So

y = KL/g

But when I place the numerical data, the result is completily different from what the writers wrote, as I sad above.

Hi Planck const!

A lump of ice falls into a lake whose temperature is 0 degrees Celsius.

A proportion K of the mass of the lump melts ( = M that melt/M )

What is the height from which the lump fell ?

perhaps the units needed converting?

Can you show us your own calculations, and also the figure given for L, and the result given in the book?

The initial temperature of the lake water = 0 C deg'
L of water = 79.7 cal/gr
K in the book = 5*10^-3 (no units)
g = 980 cm/sec^2

The answer in the book is the the height, h = 171 m = 17,100 cm (!)

Now all the potential energy become kinetic and its become thermal energy.
The thermal energy that goes from the body to the lake caused from the melting and the change in the temerature...
On those things my calculations were based .

Hi Planck const!

(have a degree: ° and try using the X2 icon just above the Reply box )

How did you convert each of those units (cal/gr and cm/s2) to SI units (or cgs units)?

Let's see...
cal = 4.2 J
so I need to multiply L in 4.2
and I get:
h (cm) = K*L*4.2 / g = 4.2 * 5 * 10^-3 * 79.7 / 980
Using pocket calculator, h = 1.83 * 10^-3 (cm) !
In the book - 1.7 * 10^+3

About the math singles in this forum... I am used to the way that I write. Thanks anyway :)

$$\frac{79.7 cal}{g} \times \frac{4.187 J}{cal} \times \frac{1000 g}{kg} = ?$$

Ok

Need erg and not Jaul ...

1 cal = 4.2 J = 4.2*10^7 erg

K*L / g = 5*10^-3 * 79.7 * 4.2*10^7 / 980 = 17,025 cm = 170.25 m

Thank you very much!

## What is the Thermodynamics Problem - the lake :P?

The Thermodynamics Problem - the lake :P is a thought experiment used to illustrate the principles of thermodynamics in a real-life scenario.

## What is the main objective of the Thermodynamics Problem - the lake :P?

The main objective of the Thermodynamics Problem - the lake :P is to understand the concept of energy transfer and how it affects the temperature of a system.

## How does the Thermodynamics Problem - the lake :P work?

The scenario involves a lake with a constant temperature and a person swimming in it. As the person swims, they generate heat which is transferred to the lake. The question is, how much will the temperature of the lake rise due to this energy transfer?

## What are the key principles of thermodynamics involved in the Thermodynamics Problem - the lake :P?

The key principles of thermodynamics involved in this problem include the conservation of energy which states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another. The second law of thermodynamics also plays a role as it states that in any energy transfer, some energy will be lost as heat.

## What can we learn from the Thermodynamics Problem - the lake :P?

Through this problem, we can learn about the concepts of energy transfer, heat transfer, and how they relate to changes in temperature. We can also gain a deeper understanding of the principles of thermodynamics and how they apply to real-world situations.

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