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
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")))#