Question

How much energy does it take to heat 346g of steam at 100 degree to steam at 110 degrees Celsius if the specific heat of the steam is $2.01{\text{ J/}}{{\text{g}}^ \circ }{\text{C}}$ ?

Answer 1

Specific heat of a body is the amount of heat required to change the heat content of exactly 1 gram of a material by exactly $1^\circ C$ . Mathematically it is the ratio of the heat capacity of a sample divided by the mass of the sample. The SI unit of specific heat capacity of a body joule per kelvin kilogram ${\text{J/Kkg}}$ . The specific heat varies with the change in temperature of a body by,
$c = \dfrac{1}{M}\dfrac{{dQ}}{{dT}}$ .

Formulas used: We will be using the formula to find the heat energy of a thermodynamic system, $q = mc\Delta T$ where $q$ is the heat energy supplied to or from the system, $m$ is the mass of the substance, $c$ is the specific heat capacity of the system, and $\Delta T$ is the change in temperature of the system.

Complete Step by Step answer
We know that heat is a form of energy and can be supplied from or to a system. Just like every other form of energy the heat energy can be transferred with a system and thus stays conserved following the law of conservation of energy.
We also know that the specific heat is a measure of the amount of heat required to technique the temperature of a system by a unit temperature. From the problem we can infer that the mass of steam is $346g$ and the system is heated from $100^\circ C$ to $110^\circ C$ .
The heat energy of the system can be found by the formula, $q = mc\Delta T$ . Substituting the known values, we get,
$q = 346 \times 2.01 \times \left( {110 - 100} \right)$
$q = 346 \times 2.01 \times 10$
Thus, solving the equation, we get,
$\Rightarrow q = 6954.6J$
Thus, the energy supplied to the steam to raise its temperature by $10^\circ C$ is $q = 6954.6{\text{J}}$ .

Note
The transfer of heat energy in a system is better explained by the first law of thermodynamics and is closely related to the law of conservation of energy. Except it involves heat energy, the thermodynamic work done on the system, and a property called the internal energy of the system.