Question

10 g samples of three different metals, each initially at 20 °c, are left in the sun for 10 minutes. the temperatures of the samples are then measured at 36 °c, 27 °c, and 41 °c respectively. which one has the highest specific heat? all three samples have the same specific heat. sample a (36 °c) sample c (41 °c) sample b (27 °c)

Explanation:

Step1: Recall the heat formula

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

Step2: Analyze the given conditions

All samples have the same mass (\( m = 10\space g \)) and are exposed to the sun for the same time, so they absorb the same amount of heat (\( Q \) is constant).

Step3: Relate specific heat and temperature change

From \( Q = mc\Delta T \), if \( Q \) and \( m \) are constant, \( c \) is inversely proportional to \( \Delta T \) (i.e., \( c \propto \frac{1}{\Delta T} \)).

Step4: Calculate temperature changes

• For sample A: \( \Delta T_A = 36 - 20 = 16\space ^\circ C \)
• For sample B: \( \Delta T_B = 27 - 20 = 7\space ^\circ C \)
• For sample C: \( \Delta T_C = 41 - 20 = 21\space ^\circ C \)

Step5: Determine the highest specific heat

Since \( c \) is inversely proportional to \( \Delta T \), the smallest \( \Delta T \) corresponds to the highest \( c \). Sample B has the smallest \( \Delta T \) (7 \( ^\circ C \)), so it has the highest specific heat.

Answer:

sample B (27 °C)