Question

in a science class, students tested how different materials heat up. they added the same amount of heat energy to three different objects that all had the same mass. the table below shows the change in temperature for each object. based on this table, which statement correctly compares the specific heat of the three objects? object x has the lowest specific heat because it has the smallest temperature change. object y has the highest specific heat because it has the smallest temperature change. object y has the lowest specific heat because it has the greatest temperature change. object z has the lowest specific heat because it has the greatest temperature change.

Explanation:

Step1: Recall the formula for heat energy

The formula for heat energy is \(Q = mc\Delta T\), where \(Q\) is the heat energy, \(m\) is the mass, \(c\) is the specific heat, and \(\Delta T\) is the change in temperature.

Step2: Analyze the relationship between specific heat and temperature change

Since \(Q\) (heat energy) and \(m\) (mass) are the same for all three objects (\(Q_{X}=Q_{Y}=Q_{Z}\) and \(m_{X} = m_{Y}=m_{Z}\)), we can rewrite the formula as \(c=\frac{Q}{m\Delta T}\). This shows that \(c\) (specific heat) is inversely proportional to \(\Delta T\) (change in temperature). That is, the object with the largest \(\Delta T\) has the smallest \(c\) (specific heat), and the object with the smallest \(\Delta T\) has the largest \(c\).

Step3: Compare the temperature changes

Object \(X\) has \(\Delta T = 7.5^{\circ}C\), object \(Y\) has \(\Delta T=15^{\circ}C\), and object \(Z\) has \(\Delta T = 10^{\circ}C\). Since \(15^{\circ}C>10^{\circ}C > 7.5^{\circ}C\) (i.e., \(\Delta T_{Y}>\Delta T_{Z}>\Delta T_{X}\)), then \(c_{Y}

Answer:

Object \(Y\) has the lowest specific heat because it has the greatest temperature change.