# Question #8e7c8

##### 1 Answer

#### Explanation:

The idea here is that you need to calculate how much heat is required in order to

convert your sample of ice at#-35^@"C"# to ice at#0^@"C"# convert the ice at#0^@"C"# to liquid water at#0^@"C"#

In order to be able to calculate the heat required in both cases, you need to know the **specific heat** of ice and the **heat of fusion** of water

#c_"ice" = "2.06 J g"^(-1)""^@"C"^(-1)#

#DeltaH_"fus" = "334.16 J g"^(-1)#

So, a substance's **specific heat** tells you how much heat is needed in order to increase the temperature of

In this case, ice has a specific heat of

Your tool of choice here will be this equation

#color(blue)(|bar(ul(color(white)(a/a)q = m * c * DeltaTcolor(white)(a/a)|)))" "# , where

*change in temperature*, defined as the difference between the **final temperature** and the **initial temperature**

In your case, you have a change in temperature of

#DeltaT = 0^@"C" - (-35^@"C") = 35^@"C"#

Plug in your values to find

#q_1 = 98.0 color(red)(cancel(color(black)("g"))) * "2.06 J" color(red)(cancel(color(black)("g"^(-1)))) color(red)(cancel(color(black)(""^@"C"^(-1)))) * 35color(red)(cancel(color(black)(""^@"C")))#

#q_1 = "7,065.8 J"#

Now, adding this much heat to **ice** at *melt the ice*, you must provide it with enough heat to allow it to undergo a *solid* *liquid* phase change.

The **heat of fusions**, *per gram* of solid ice at

Since you have

#98.0 color(red)(cancel(color(black)("g"))) * overbrace("334.16 J"/(1color(red)(cancel(color(black)("g")))))^(color(blue)(=DeltaH_"fus")) = "32,748 J"#

The **total amount of heat** needed to get your sample from ice at

#q_"total" = "7,065.8 J" + "32,748 J"#

#q_"total" = "39,814 J"#

I'll leave the answer rounded to three **sig figs**

#"the amount of heat needed" = color(green)(|bar(ul(color(white)(a/a)color(black)("39,800 J")color(white)(a/a)|)))#