Question

The specific heat of ice is ${\text{0}}{\text{.5calories/gra}}{{\text{m}}^{\text{0}}}{\text{C}}$ ? 20 grams of ice will require how many calories to raise the temperature ${1^{\text{0}}}{\text{C}}$ ?

Answer 1

We are already provided with the specific heat of ice. The measurement of heat is called calorimetry. The calorie, or gram calorie, is the quantity of heat required to raise the temperature of 1 gram of pure water ${1^{\text{0}}}{\text{C}}$ . The kilocalorie, or kilogram calorie, is the quantity of heat required to raise the temperature of 1 kg of pure water ${1^{\text{0}}}{\text{C}}$ .

Complete step by step solution:
We are provided with the specific heat and it is expressed in units of energy, in this case calories, per gram Celsius, which means that a substance's specific heat tells we how much energy is needed to increase the temperature of 1 g of said substance by ${1^{\text{0}}}{\text{C}}$ .
For ice, we know that if we provide $0.5$ calories of heat to 1 g of ice we will increase its temperature by ${1^{\text{0}}}{\text{C}}$ .
To increase the temperature of 20 g of ice by, ${1^{\text{0}}}{\text{C}}$ we need to provide it with $0.5$ cal for every gram. This will cause its temperature to increase by ${1^{\text{0}}}{\text{C}}$ .
${{20g \times }}\dfrac{{{\text{0}}{\text{.5ca}}{{\text{l}}^{\text{0}}}{{\text{C}}^{{\text{ - 1}}}}}}{{{\text{1g}}}}{\text{ = 10ca}}{{\text{l}}^{\text{0}}}{{\text{C}}^{{\text{ - 1}}}}$
And for ${1^{\text{0}}}{\text{C}}$ increase in temperature we have 10cal.
As we can see, to increase the temperature of this sample by ${1^{\text{0}}}{\text{C}}$ more than you need to provide it with 10 cal of heat for every ${1^{\text{0}}}{\text{C}}$ increase in temperature.
${3^{\text{0}}}{\text{C}} \times \dfrac{{10{\text{cal}}}}{{{1^{\text{0}}}{\text{C}}}} = 30{\text{cal}}$
Therefore, you can say that in order to increase the temperature of 20 g of ice by ${3^{\text{0}}}{\text{C}}$ , you need to provide it with 30 cal of heat.

Additional Note
We should know about the effect of heat on changing temperature. For example: exercising in hot weather puts extra stress on your body. If we don't take care when exercising in the heat, we risk serious illness. Both the exercise itself and the air temperature and humidity can increase your core body temperature. To help cool itself, our body sends more blood to circulate through your skin.
The reason behind this is if we heat a substance, the particles move faster and so collide more frequently. That will speed up the rate of reaction.

Note:
We already know that when the reactants are heated, the average kinetic energy of the molecules increases. This means that more molecules are moving faster and hitting each other with more energy. If more molecules hit each other with enough energy to react, then the rate of the reaction increases. An increase in the temperature of a system favours the direction of the reaction that absorbs heat, the endothermic direction. Absorption of heat in this case is a relief of the stress provided by the temperature increase.