Chapter U5.102, Problem 2E

Interpretation Introduction

Interpretation: The importance of the specific heat of a substance being heated by the combustion of a given fuel needs to be explained.

Concept Introduction: The specific heat of a substance is defined as the amount of heat required to heat unit mass (usually 1 gram) of the substance by unit degree (usually 1°C or 1 K). The specific heat of the substance is an important property in determining the amount of heat absorbed by the substance.

Answer to Problem 2E

The specific heat of the substance is important because it dictates the temperature rise of a given mass of the substance caused by the combustion of the fuel or alternatively, the mass of the substance heated to affect a specific temperature change of the substance.

Explanation of Solution

The principal of thermochemistry states that the heat lost by a hot substance is equal and opposite to the heat gained by a cold substance when the two substances are brought in contact. In other words, the heat energy is conserved when the two substances are brought close to each other.

In this example, a specific mass of a fuel is combusted and the combustion of the fuel generates an amount of heat energy, say Q (in Joules for example). The heat energy resulting from the combustion of the fuel is used to heat a substance having a specific heat capacity of say, S (in J/g.K for example).

Since the specific heat of the substance is S, hence, it is imperative that C Joules of heat energy is required to heat 1 g of the said substance by 1 K or 1°C.

Again, as per the principal of thermochemistry, it may be stated,

  $q=mc\Delta T$

Here, m is mass of the substance in grams, S(J/g.°C is specific heat capacity and $\Delta T$ is change temperature of the substance in °C.

If the mass of the substance is known, then the rise in temperature of the substance being heated can be easily predicted from the above expression. Thus, the final temperature of the substance may be easily determined if the initial temperature of the substance is known.

Alternative, if the rise in temperature of the substance being heated is known, then the mass of the substance heated can be easily determined from the above expression.

Finally, the specific heat of a substance can be used to calculate the time required to heat the substance. If the heating rate provided by the heating source is known, then the time required to heat the substance can be easily calculated. The later point is particularly important in industries where combustion of a certain fuel is often used to power a chemical reaction.