# How many calories are required to raise the temperature of a 35.0 g sample of iron from 25°C to 35°C? Iron has a specific heat of 0.108 cal/g°C?

##### 1 Answer

#### Explanation:

The key to this problem lies in the value of the **specific heat** of iron.

#c_"iron" = "0.108 cal"# #color(blue)("g"^(-1))color(darkorange)(""^@"C"^(-1))#

This tells you that in order to increase the temperature of *one unit of mass* of iron, i.e. of *one unit of temperature*, i.e. by

Now, you can use the specific heat of iron to figure out the amount of heat needed to increase the temperature of

#35.0 color(red)(cancel(color(black)("g"))) * "0.108 cal"/(color(blue)(1)color(red)(cancel(color(blue)("g"))) * color(darkorange)(1^@"C")) = "3.78 cal"# #color(darkorange)(""^@"C"^(-1))#

This tells you that in order to increase the temperature of

In your case, the temperature of the iron must increase by

#35^@"C" - 25^@"C" = 10^@"C"#

which means that you will need

#10color(red)(cancel(color(black)(""^@"C"))) * "3.78 cal"/(color(darkorange)(1)color(red)(cancel(color(darkorange)(""^@"C")))) = "37.8 cal"#

Now, you should round the answer to *one significant figure*, the number of **sig figs** you have for the **change in temperature**, i.e. for

#color(darkgreen)(ul(color(black)("heat needed = 38 cal")))#