Question

How do you determine the mass of water sample that is heated from an initial temperature of $\mathbf{2}{{\mathbf{5}}^{\mathbf{o}}}\mathbf{C}$ to a final temperature of $\mathbf{100{}^\circ C}$ following the addition of $\mathbf{1200}\,\mathbf{J}$ of heat energy?

Answer 1

Heat energy can be transferred from one object to another. The transfer or flow due to the difference in temperature between the two objects is called heat. The thermal energy Q is directly proportional to the mass of the substance, temperature difference, and the specific heat. SI unit of thermal energy is Joules (J) formula is given by $\text{Q}=\text{m}{{\text{C}}_{\text{p}}}\Delta \text{T}\text{.}$ Q is heat variable, m is the mass, ${{\text{C}}_{\text{p}}}$ is the specific heat and $\Delta \text{T}$ is change in temperature.

Complete step by step answer:
It is given the initial temperature is $25{}^\circ \text{C}$ i.e. ${{\text{T}}_{1}}$ and final temperature is $100{}^\circ \text{C}$ i.e. ${{\text{T}}_{2}}$. Heat energy $\text{Q}=\text{1200}\,\text{J}$, we need to calculate the mass as follows;
We have the formula for heat absorbed as $\text{Q=m}{{\text{C}}_{\text{p}}}\Delta \text{T}$ where m is mass, ${{\text{C}}_{\text{p}}}$ is specific heat, $\Delta \text{T}$ is the temperature change. ${{\text{C}}_{\text{p}}}$ of water is $4.184\ \text{j/g}{}^\circ \text{C}$
By substituting all the values is the formula we get,
$\text{Q}=\text{m}\times \text{4}\text{.184}\dfrac{\text{J}}{\text{g}{}^\circ \text{C}}\times 75$
$1200=\text{m}\times \text{4}\text{.184}\times \text{75}$
$\text{m}=\text{3}\text{.8g}$
Therefore mass of the water is $3.8\,\text{g}\text{.}$
Different materials would warm up at different rates because each material has its own specific heat capacity. The specific heat capacity refers to the amount of heat required to cause a unit of mass to change its temperature by $1{}^\circ \text{C}$. The quantity of energy transferred as heat in a process is the amount of transferred energy excluding any thermodynamic work that was done and energy contained in matter transferred.

Additional Information:
The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies or radiation between separated bodies. Heat transfer is generally described as including the mechanism of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes. Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process. The transferred heat is measured by changes in a body of known properties. First law of thermodynamics states that the change in internal energy $\Delta \text{V}$ of the system is equal to the amount of heat supplied to the system minus the amount of work done by the system on its surrounding.

Note: When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately and spontaneously from the hotter to colder system.
Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body. Heat released by a system into its surroundings is by convention a negative quantity; when a system absorbs heat from its surroundings, it is positive. At a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate. In such cases, cooling has the reverse effect.