Find Final Water Temp: Heat of Fusion

[doggieslover]

Part E
In an insulated container, 0.50 \rm kg of water at 80^\circ \rm C is mixed with 0.050 \rm kg of ice at -5.0^\circ \rm C. After a while, all the ice melts, leaving only the water. Find the final temperature T_f of the water. The freezing point of water is 0^\circ \rm C.
Express your answer in degrees Celsius to two significant figures.

Okay, so I know I have to use heat of fusion, Q=mL, and I know Qnet = 0, but I am not sure how to combine these info together.

What I have is. . . (I converted everything to K first)
m_1c_1deltaT + m_2c_2deltaT + mL = 0
(.5kg)(4184J/kgK)(T_f-353K)+(.05kg)(2050J/kgK)(T_f-286K)+mL = 0
I am not sure if I have plugged in the values correctly and I don't know what m and L is. . .

Please help?

 

[naresh]

1. L is the Latent Heat of fusion of water - this is a well known quantity. Look it up in your textbook or on the web.

2. Think about what happens to the ice. What temperature does it heat up to? What happens then?

 

[doggieslover]

Ok so I found the heat of fusion for water's melting point is 334kJ/kg, so I converted it to 334000J/kg. But I am still unsure if I have up the equation right, and also which mass do I use for the (mL) part, I picked .5kg, because that is the object BEING mixed with the ice. But I am not sure.

m_1c_1deltaT + m_2c_2deltaT + mL = 0
(.5kg)(4184J/kgK)(T_f-353K)+(.05kg)(2050J/kgK)(T_f-286K)+ (.5kg)(334000J/kg) = 0

 

[naresh]

No, the latent heat is the heat required to change the state of the substance (here, from solid to liquid). What mass undergoes this change?

Take a step back from the equation and try and describe the physical process. What do you think happens to the 0.5 kg of water? What happens to the 0.05 kg of ice?

 

[doggieslover]

The .05kg of ice will melt, so the L of that will be 334Kj/ kg?

 

[naresh]

yes, that is right. What happens to the ice before and after melting?

 

[doggieslover]

The ice changes phase from solid to liquid?

Does that mean there will be two Q = mL equations?

 

[naresh]

No, Q=mL describes the phase change, so there is no second equation.

The ice was at -5 degrees, right? At what temperature does it change phase? What happens in the meantime? What happens after it melts?

 

[doggieslover]

temp of ice will increase to its melting point, then the temperature of the melted ice will keep increasing until it reaches the final temperature. That's all I know, but I still don't know how to apply all this info. .

 

[doggieslover]

So, I set up the equation as:

mcdeltaT (ice) + mL (ice, heat of fusion) - mcdeltaT (water from the melted ice) = mcdelta (water from system)

and I keep getting T as 80C (which is incorrect) and I am not sure why.