Can you go over #q = m * c * DeltaT# ?

1 Answer

The specific heat capacity, or simply specific heat #(C)# of a substance is the amount of heat energy required to raise the temperature of one gram of the substance by one degree Celsius. Heat energy is usually measured in Joules #("J")# or calories #("cal")#.

The variables in the equation #q = mCDeltaT# mean the following:

#" let:"#
#q="heat energy gained or lost by a substance"#
#m="mass (grams)"#
#C="specific heat"#
#DeltaT="change in temperature"#

Note that #DeltaT# is always calculated as #"final temperature "-" initial temperature"#, not the other way around.

Therefore, you can look at that equation like this if it helps:

#"heat energy gained or lost by a substance"=("mass")("specific heat")(DeltaT)#

Example
How much heat energy is required to raise the temperature of #"55.0g"# of water from #"25.0"^@"C"# to #"28.6"^@"C"#? The specific heat of water is #"4.18""J"#/#"g"^@"C"#. This is a very well known specific heat value and will frequently show up in specific heat questions.

Unknown:
#q# in Joules #("J")#

Known/Given:
specific heat of water #(C)# = #"4.18""J"#/#"g"^@"C"#
mass of water = #"55.0g"#
#DeltaT# = #"28.6"^@"C"-"25.0"^@"C"# = #"3.6"^@"C"#

Equation:
#q =mcDeltaT#

Solution:
#q="55.0g" xx "4.18""J"#/#"g"^@"C"xx"3.6"^@"C"#
#q# = #"827.64""J"#, which rounds to #8.28xx10^2"J"# due to significant figures.


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