Question

\metal ice cubes\ are sometimes used to avoid diluting beverages, but they arent all that effective. 50 g of each metal at -5 °c are added to 100 ml of a beverage at 10 °c. which metal has the greatest cooling effect?
metal | specific heat (j/g°c)
al | 0.900
brass | 0.380
sn | 0.240
au | 0.129
options: tin, brass, gold, aluminum

Explanation:

To determine which metal has the greatest cooling effect, we use the formula for heat transfer, \( Q = mc\Delta T \), where \( Q \) is the heat absorbed by the metal, \( m \) is the mass of the metal, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

Step 1: Identify the values

• Mass of each metal, \( m = 50 \, \text{g} \)
• Initial temperature of the metal, \( T_{\text{initial, metal}} = -5^\circ \text{C} \)
• Temperature of the beverage, \( T_{\text{beverage}} = 10^\circ \text{C} \)
• So, the change in temperature for the metal, \( \Delta T = T_{\text{beverage}} - T_{\text{initial, metal}} = 10 - (-5) = 15^\circ \text{C} \) (since the metal will absorb heat from the beverage, causing the beverage to cool)

Step 2: Analyze the formula for heat absorbed by the metal

The heat absorbed by the metal, \( Q \), is given by \( Q = mc\Delta T \). For all metals, \( m \) (50 g) and \( \Delta T \) (15 \(^\circ\)C) are the same. Therefore, \( Q \) is directly proportional to the specific heat capacity \( c \) of the metal. A higher specific heat capacity means more heat is absorbed from the beverage, resulting in a greater cooling effect on the beverage.

Step 3: Compare the specific heat capacities

Looking at the specific heat values:

• Aluminum (Al): \( 0.900 \, \text{J/g}^\circ\text{C} \)
• Brass: \( 0.380 \, \text{J/g}^\circ\text{C} \)
• Tin (Sn): \( 0.240 \, \text{J/g}^\circ\text{C} \)
• Gold (Au): \( 0.129 \, \text{J/g}^\circ\text{C} \)

Aluminum has the highest specific heat capacity among the given metals. Since \( Q \propto c \) (when \( m \) and \( \Delta T \) are constant), aluminum will absorb the most heat from the beverage, leading to the greatest cooling effect on the beverage.

Answer:

D. aluminum (where D is the option for aluminum)