Calculate Heat Energy Req'd for 0.1 kg Ice -30°C to 0°C

[kingstar]

Homework Statement

Calculate the heat energy required to convert 0.1 kg of ice at -30°C into water at 0°C. The
specific heat capacity of ice is 2100 J kg-1K-1
and the latent heat of fusion of ice is 3.25 x 10^5 J kg-1

Homework Equations

e=mcθ

The Attempt at a Solution

So first i did
e = 0.1 x 2000 x 30 = 6300.

I'm sure I am missing something because I haven't used the latent heat of fusion of Ice? and I'm not sure why i would need that :S

 

[rock.freak667]

You will need to get the energy required to heat the ice from -30 to 0 + energy required to change the ice to water (this is where the latent heat comes in)

 

[CWatters]

There are two steps..

1) Heat required to warm the ice from -30 to 0C. This depends on the Specific Heat Capacity of ice. You were correct except for the typo and missing units..

e = 0.1 x 2100 x 30 = 6300Joules

2) Heat required for the phase change (eg to melt the ice to water) while it remains at 0C. This depends on the Latent heat of fusion of ice/water which is ..

= 0.1 x 3.25 x 10^5 = 32500 Joules.

Add the two figures together together to get the answer.

Aside: The Latent heat of fusion and Latent heat of vapourisation of water are quite high. One reason why steam is dangerous is that a heck of a lot of energy is given out when the steam condenses to water on your skin. The heat given out by steam condensing is roughly 10 times that given out when the resulting water cools from say 100C to body temperature.

 

[kingstar]

Ahhhhhhhh thanks
i forgot the phase change completely!

Makes sense now, thank you!

 

[Nickie]

Your attempt at a solution is partially correct. You have correctly used the specific heat capacity of ice (2100 J kg-1K-1) to calculate the energy required to raise the temperature of 0.1 kg of ice by 30 degrees Celsius (e=mcθ). This gives you the amount of energy required to convert the ice at -30°C to ice at 0°C.

However, to fully convert the ice into water at 0°C, you also need to take into account the latent heat of fusion of ice (3.25 x 10^5 J kg-1). This is the amount of energy required to change the state of the substance from solid to liquid, without changing its temperature.

So, to calculate the total heat energy required, you need to add the energy required for the temperature change (6300 J) to the energy required for the phase change (3.25 x 10^5 J). This gives you a total of 3.31 x 10^5 J.

Therefore, the heat energy required to convert 0.1 kg of ice at -30°C to water at 0°C is 3.31 x 10^5 J.