What quantity of heat energy must have been applied to a block of aluminum weighing 42.7 g if the temperature of the block of aluminum increased by 15.2°C?

1 Answer
Mar 11, 2016

Answer:

#"591 J"#

Explanation:

As it stands, the problem fails to provide you with an essential piece of information - the value of aluminium's specific heat.

This means that you're going to have to track it yourself. You can find it listed here

http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

as being equal to

#c = "0.91 J g"^(-1)""^@"C"^(-1)#

So, a substance's specific heat tells you how much heat is needed in order to increase the temperature of #"1 g"# of that substance by #1^@"C"#.

In this case, you need to provide aluminium with #"0.91 J"# of heat in order to increase the temperature of #"1 g"# by #1^@"C"#.

You know that the block of aluminium has a mass #"42.7 g"#. This means that if you were to increase its temperature by just #1^@"C"#, you'd need

#42.7 color(red)(cancel(color(black)("g"))) xx "0.91 J" color(red)(cancel(color(black)("g"^(-1))))""^@"C"^(-1) = "38.86 J" ""^@"C"^(-1)#

This much heat would increase the temperature of #"42.7 g"# of aluminium by #1^@"C"#. To increase its temperature by #15.2^@"C"#, you'd need #15.2# times more heat

#15.2color(red)(cancel(color(black)(""^@"C"))) xx "38.86 J" color(red)(cancel(color(black)(""^@"C"^(-1)))) = "590.67 J"#

Rounded to three sig figs, the answer will be

#"heat needed" = color(green)(|bar(ul(color(white)(a/a)"591 J"color(white)(a/a)|)))#

Alternatively, you can use the formula

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

#q# - the amount of heat added / removed
#m# - the mass of the sample
#c# - the specific heat of the substance
#DeltaT# - the change in temperature

Plug in your values to get

#q = 42.7 color(red)(cancel(color(black)("g"))) * "0.91 J" color(red)(cancel(color(black)("g"^(-1))))color(red)(cancel(color(black)(""^@"C"^(-1)))) * 15.2color(red)(cancel(color(black)(""^@"C")))#

#q = color(green)(|bar(ul(color(white)(a/a)"591 J"color(white)(a/a)|)))#