Thermal physics -- Latent heat melting ice

[Cici2017]

Homework Statement

Question (b) (iii)

Homework Equations

The Attempt at a Solution

The energy required to melt the ice is
Q1=mL=3*0.025*3.3*10^5=24750J
The energy released by water is
Q2=mcT=0.33*4200*(22-T)

Shall I calculate the energy that the ice needs after it melts into water?
i.e. Q3=0.075*4200*(0-T)

So Q1+Q3=Q2 and then just solve for T?

Is that right? I did it this way but got a different answer to the mark scheme.

 

[DoItForYourself]

Will the final temperature T be greater or lower than 0°C?

 

[Chestermiller]

Do the calculation assuming that all the ice melts. If the final calculated temperature comes out above 0C, you're through. What if the final calculated temperature comes out below 0C? Then what can you say about the final temperature? How does this change the calculation?

 

[Cici2017]

Will the final temperature T be greater or lower than 0°C?

Should be greater than 0

 

[Cici2017]

Do the calculation assuming that all the ice melts. If the final calculated temperature comes out above 0C, you're through. What if the final calculated temperature comes out below 0C? Then what can you say about the final temperature? How does this change the calculation?

What calculations do I need to do?

 

[Chestermiller]

What calculations do I need to do?

Your expression for Q3 has the wrong sign.

So, what do you get when you solve your equations for T?

 

[Cici2017]

Your expression for Q3 has the wrong sign.

So, what do you get when you solve your equations for T?

T＝4.05

 

[Chestermiller]

T＝4.05

Good. When you substitute this back into your equations, does this satisfy them?

 

[Cici2017]

Good. When you substitute this back into your equations, does this satisfy them?

um... not quite. I got Q1+Q3=26025.75 and Q2=24878.7

 

[DoItForYourself]

Should be greater than 0

Yes, in case the ice melts completely, the temperature should be greater than 0°C. If the ice does not melt compeltely, this means that the thermal energy of the water is not enough and its initial temperature must be increased in order to melt completely the ice.

 

[haruspex]

T＝4.05

As you found, this is not right. Please post your working.

 

[Cici2017]

As you found, this is not right. Please post your working.

I followed the logic in my attempt. Is that wrong or is there something wrong in my calculation?

 

[haruspex]

I followed the logic in my attempt. Is that wrong or is there something wrong in my calculation?

Did you correct the sign error pointed out in post #6?
If so, you should have got the right answer. I cannot tell where you went wrong without seeing your working.