# What is the specific heat capacity of a metal if it requires 178.1 J to change the temperature to 15.0 g of the metal from 25.00 C to 32.00 C?

##### 1 Answer

#### Explanation:

When a problem asks you to find a substance's **specific heat**,

In your case, you know that you need

#DeltaT = 32.00^@"C" - 25.00^@"C" = 7.00^@"C"#

So, how much heat would be needed to increase the temperature of

#1 color(red)(cancel(color(black)("g"))) * "178.1 J"/(15.0color(red)(cancel(color(black)("g")))) = "11.873 J"#

Since this much heat is needed to increase the temperature of

#1color(red)(cancel(color(black)(""^@"C"))) * "11.873 J"/(7.00color(red)(cancel(color(black)(""^@"C")))) = "1.70 J"#

Since you need **specific heat** will be

#c = color(green)(|bar(ul(color(white)(a/a)color(black)("1.70 J g"^(-1)""^@"C"^(-1))color(white)(a/a)|))) -> # rounded to threesig figs

**ALTERNATIVELY**

You can also use the following 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**

Rearrange to solve for

#q = m * c * DeltaT implies c = q/(m * DeltaT)#

Plug in your values to find

#c = "178.1 J"/("15.0 g" * 7.00^@"C") = color(green)(|bar(ul(color(white)(a/a)color(black)("1.70 J g"^(-1)""^@"C"^(-1))color(white)(a/a)|)))#