Calculating Phase Transitions in a Water-Ice Mixture

In summary, the conversation discusses how to calculate the amount of ice that needs to melt in order to lower the temperature of 500 mL of water to 0°C. The specific heat capacity of ice and latent heat are considered, and the final solution is calculated using the equation Q=mcΔt + mL. The final answer is determined to be 157 grams of ice.
  • #1
liz_p88
18
0

Homework Statement



Ice at 0°C is mixed with 5 x 10^2 mL of H2O at 25°C. How much ice must melt to lower the H2O temp to 0°C?

Homework Equations



mcΔt = -[mcΔt]

The Attempt at a Solution



(500ml)(4.186 kJ/kg*K)(-25) = m(2.1 kJ/kg*K)(25)


996 ml or gram equivalents

I know this is wrong but I can't figure out how to do it
 
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  • #2
Why use the specific heat capacity of ice? The ice isn't changing temperature, it's undergoing a phase change. Think latent heat.
 
  • #3
Thats where I get confused. Okay so because of latent heat, I would have to use the equation...mcΔt + mL + mcΔt = -[mcΔt]...or Q=mcΔt + mL? This is where I get confused. The only thing is, I don't know how to plug in the variables. I know it takes 333.7 kJ to change 1 kg of ice to water at 0 celcius
 
  • #4
liz_p88 said:
I know it takes 333.7 kJ to change 1 kg of ice to water at 0 celcius

Maybe this is the best place to start reasoning, rather than monkeying around with the equations. Assuming 1 g of ice melts, what would be the temperature change of 500 g of water? Can you continue from there?
 
  • #5
Ok I think I have it. Q gained by the ice = Q lost by the water
mLf + mc(Tf - 0) = mc(Ti - Tf)

m(333.7) + mc(0-0) = (500)(4.186)(25)

= 157 g
 
  • #6
Nice.
 

1. What is a phase transition in relation to mcΔt?

A phase transition refers to the change in physical state or properties of a substance due to a change in temperature or pressure. In the context of mcΔt, phase transitions occur when there is a change in the thermal energy of a system, leading to a change in its state or properties.

2. How is mcΔt related to phase transitions?

mcΔt, or the change in thermal energy, is directly related to phase transitions as it is the driving force behind the change in state or properties of a substance. In order for a phase transition to occur, there must be a change in thermal energy, which is represented by the mcΔt term in the equation.

3. What are the different types of phase transitions?

There are several types of phase transitions, including solid-liquid, liquid-gas, solid-gas, and plasma transitions. Each type is characterized by a change in the physical state or properties of a substance, such as melting, boiling, or sublimation.

4. How does the rate of temperature change affect phase transitions?

The rate of temperature change, represented by Δt, plays a crucial role in phase transitions. A faster rate of temperature change can lead to more rapid phase transitions, while a slower rate may result in a gradual transition. This is due to the amount of energy needed for the phase transition to occur.

5. Can phase transitions be reversed?

Yes, phase transitions can be reversed by changing the conditions that caused the transition in the first place. For example, if a substance undergoes a solid-liquid phase transition due to an increase in temperature, it can be reversed by decreasing the temperature back to its original state. This is known as a reversible phase transition.

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