# Question 94dc7

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:

$Q = c \cdot m \cdot \Delta T$

$c =$specific heat = for one gram, one degree difference
multiply by:
$m =$mass, the amount of grams you want to warm up
multiply again by:
$\Delta T =$the temperature rise you wish

$Q = c \cdot m \cdot \Delta T = 2.46 \cdot 193 \cdot \left(35 - 19\right) \approx 7596 J$

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 - ${19}^{\circ} \text{C}$ and $\text{35"^@"C}$; 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 ${16}^{\circ} \text{C}$, 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

$q = m \cdot c \cdot \Delta T$, 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;
$\Delta T$ - the change in temperature;

To determine how much energy is required to heat 193 g of ethanol by ${16}^{\circ} \text{C}$, plug your values into the above equation

$q = \text{193"cancel("g") * 2.46"J"/(cancel("g") * ^@cancel("C")) * 16^@cancel("C") = "7596.48 J}$

Rounded to two sig figs, the number of sig figs given for 19 and 35 degrees Celsius, the answer will be

$q = \textcolor{g r e e n}{\text{7600 J}}$

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):

$193 g \times 2.46 \frac{J}{g - C} \times 16 C = 7596 J$