Solving Heat Transfer Problem with Melting Ice Cube

[david98999]

Good day members of physics forums .

I am a university student currently studying thermodynamics and I just am a bit confused about a heat transfer problem.

If you have the following items: 1 metal container which is well insulated from the outside ;
; 1 quantity of water and an icecube .

The water and the metal container are at 22 degrees celsius .
The ice cube is at the melting point 0 degrees celsius

The ice is added to the metal container and when thermal equilibrium is reached the temperature of the system is 15 degrees.

the heat transfer equation is Q(water)+Q(ICE) +Q(container)=0 in an isolated system where the heat of the container/water increases the temperature of the ice as the container/water decrease in temperature.

now with regards to the heat tranfer of the ice Q(ICE) I am a bit confused

I believe that the equation should be Q(ICE)=change in temperature =mc(Delta T)

but I am unsure if I should add the heat of transformation equation Q=ML .I think we don't need to because the ice cube is already at room temperature but i would kindly like to verify this because I am unsure.

Thank you .

 

[Buzz Bloom]

Hi david:

I confess I did not follow all of you reasoning. However, I think you omitted the energy needed to melt the ice.

Hope this helps.

Regards,
Buzz

 

[Chestermiller]

What the heck is Q supposed to be in your equations? I though you said you are currently studying thermodynamics. If so, then you know you should be focusing on the internal energy U of the system in its initial and final states. Do you know what internal energy is, and how to calculate the change in internal energy?

 

[david98999]

What the heck is Q supposed to be in your equations? I though you said you are currently studying thermodynamics. If so, then you know you should be focusing on the internal energy U of the system in its initial and final states. Do you know what internal energy is, and how to calculate the change in internal energy?

-----------

My apologies . Q refers to the heat of transformation . I said that the net heat in this internal ice/container/water system is equal to zero .My textbook is Physics for scientists and engineers . Randall Knight 3rd edition

 

[Chestermiller]

OK. Let $m_i$, $m_w$, and $m_c$ be the initial masses of ice, water, and the container. Let the arbitrary reference state of zero internal energy (per unit mass) for ice and water be liquid water at 0 C, and the arbitrary reference state of zero internal energy (per unit mass) for the container be 0 C. So the initial internal energies per unit mass of the ice, water, and container are

$$u^0_i=-L$$
$$u^0_w=C_w(22-0)$$
$$u^0_c=C_c(22-0)$$
where the C's are the heat capacities of water and container, and L is the latent heat of melting ice.

Based on these relationships, what is the total internal energy $U^0$ of the system in its initial state?

In the final state of the system, all the ice is melted, and the total mass of liquid water is now $(m_i+m_w)$, while the final temperature of the system is 15 C. Based on this, what is the final internal energy per unit mass of the water and of the container, $u_w$ and $u_c$? What is the total internal energy of the system in its final state U?

Based on the first law of thermodynamics, how are U and $U^0$ related?

Chet