Question

A certain amount of heat \[\text{Q}\] will warm \[1\text{ g}\] of material \[\text{X}\] by \[\text{3}{}^\circ \text{C}\] and \[1\text{ g}\] of material \[\text{Y}\] by \[\text{5}{}^\circ \text{C}\], which material has greater specific heat capacity? Support answers with calculations.

Answer 1

Hint By comparing the specific heat formulas \[\left( \text{Q = mc}\Delta \text{t} \right)\] for material \[\text{X}\] and material \[\text{Y}\], the required solution can be obtained.
Formula used: \[\text{Q = mc}\Delta \text{t}\], which is a specific heat formula.

Complete Step by step solution
We know that, heat \[\text{Q}\] warms \[1\text{ g}\] of material \[\text{X}\]by \[\text{3}{}^\circ \text{C}\]. Therefore, substituting these values in specific heat formula, we get:
\[\text{Q = 1}\times \text{C}x\times 3\] …..(1)
Similarly, heat \[\text{Q}\] warms \[1\text{ g}\] of material \[\text{Y}\] by \[\text{5}{}^\circ \text{C}\], therefore
\[\text{Q = 1}\times \text{C}y\times 5\] …..(2)
As the same heat \[\text{Q}\] is provided to both the material, therefore the left hand side of equation (1) and (2) are the same. Hence, on comparing right hand sides, we get,
\[\begin{align}
  & 3\text{C}x=5\text{C}y \\
 & \text{C}x=\frac{5}{3}\text{C}y
\end{align}\]

Hence, material \[\text{X}\] has greater specific heat than material \[\text{Y}\].

Note Specific heat capacity of a substance is the heat capacity of a sample divided by mass of sample or we can say that, it is the amount of energy that must be added in the form of heat to one unit of mass of substance to cause increase of one unit in temperature.