Question #94dc7

3 Answers
Apr 1, 2015

Specific heat means the heat to raise the temperature of 1 gram of the material by 1 degree C.

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 difference
multiply by:
#m=#mass, the amount of grams you want to warm up
multiply again by:
#DeltaT=#the temperature rise you wish

Your answer:

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.

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^@"C"#

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#