Specific heat means the heat to raise the temperature of 1 gram of the material by 1 degree C.
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So if you want to raise the temperature of that one gram from 19 to 35 degrees, that same gram will need #35-19=16# times as much heat.
And if you want to raise the temperature of 193 grams in stead of just 1 gram, you will need 193 times as much heat.
These two combined give us the following equation:
#c=#specific heat = for one gram, one degree differencemultiply by:#m=#mass, the amount of grams you want to warm upmultiply again by:#DeltaT=#the temperature rise you wish
Apr 1, 2015
You know the specific heat of ethanol, which represents the amount of heat required to increase the temperature of 1 gram of ethanol by 1 degree Celsius.
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In other words, to get the temperature of 1 gram of ethanol to increase by 1 degree Celsius, you must supply 2.46 J of energy to it.
Now, you know the initial and final temperature of the sample - #19^
"C"# and #"35"^
"C"#; this means that the temperature of your ethanol sample increased by
#DeltaT = T_("final") - T_("initial") = 35 - 19 = 16^
You must supply enough energy to increase the temperature of the sample by #16^
"C"#, but you must tak into account how much ethanol you have, i.e. the mass given.
The relationship between supplied energy (or heat), mass, and increase in temperature is given by
#q = m * c * DeltaT#, where
#q# - the amount of energy supplied;#m# - the mass of the substance - in your case, the mass of ethanol;#c# - the specific heat of ethanol;#DeltaT# - the change in temperature;
To determine how much energy is required to heat 193 g of ethanol by #16^
"C"#, plug your values into the above equation
#q = "193"cancel("g") * 2.46"J"/(cancel("g") * ^
cancel("C")) * 16^
cancel("C") = "7596.48 J"#
Rounded to two sig figs, the number of sig figs given for 19 and 35 degrees Celsius, the answer will be
#q = color(green)("7600 J")#
Apr 1, 2015
The heat required is equal to the mass of ethanol (193 g) multiplied by the specific heat capacity (2.46 J/g-C) times the desired temperature difference (35 C - 19 C = 16 C):
#193 g times 2.46 J/(g-C) times 16C=7596 J#
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