Question

Question #94dc7

Answer 1

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:

`Q=c*m*DeltaT`

`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:
`Q=c*m*DeltaT=2.46*193*(35-19)~~7596J`

Answer 2

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")`

Answer 3

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`