Entropy of system with ice cube in lake

[Brunno]

An ice cube of 10g -10°C is placed in a lake that is 15°C.Calcule the variation of entropy of the system when the ice cube to reach the thermal balance with the lake.
The specific heat of the lake is 0,50cal/g°C.

 

[G01]

You have to show your work in order to get help on homework type problems here.

What have you tried so far?

Also, next time, please post homework type problems in the appropriate homework help forum.

 

[Brunno]

Ok,GO1,
I'll tell you,You might have thought about my bad English( I'm far way from you).For that,I'm sorry I really don´t write it well.:shy:.But it´s understood what you said!
Well,what have I tried so far?
This:
$$m*c\int_{Ti}^{T_f}\frac{dT}{T}$$
But I really don't understand nothing after it.I do know some concepts about derivative,but can you explain the equation above?And it's not a homework,it's just a doubt.
Thank you!

 

[Brunno]

Anyone?

 

[Brunno]

Ok,
Could somebody show me the why the darivative of $$\frac{dT}{T}$$ is equal to $$ln\frac{T_f}{T_i}$$??

 

[G01]

Ok,
Could somebody show me the why the darivative of $$\frac{dT}{T}$$ is equal to $$ln\frac{T_f}{T_i}$$??

It is the integral, not the derivative that you are finding.

HINT:
Start by letting y=ln(x)

Therefore, $$x=e^y$$

Take the derivative of both sides and you should be able to solve for dy/dx and derive the result your questioning. Specifically,

$$\frac{d \ln(x)}{dx}=\frac{1}{x}$$

So, when finding the this anti-derivative, we have:

$$\int\frac{dx}{x}=\ln{x} + C$$

This is a good formula to remember. If you don't remember, or have never learned this, you should probably review your calculus. Not knowing calculus like this will really hinder you as you try to learn more physics.