Question

two systems, one with 50.0 g of aluminum and the other 100.0 g of aluminum, are initially at 35.0°c. over a period of ten minutes, heat is added to each system and the final temperatures are both 45.0°c. compare the heat added to each system. the heat added is greater for the 50.0 g al system. the heat added is greater for the 100.0 g al system. the heat added is the same for each system. the heat cannot be interpreted from this information.

Explanation:

Step1: Recall the heat formula

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

Step2: Analyze the variables

For both aluminum systems, \( c \) (specific heat of Al) is the same, \( \Delta T = 45.0^\circ\text{C}- 35.0^\circ\text{C}=10.0^\circ\text{C} \) is the same. But \( m_1 = 50.0\space g \), \( m_2 = 100.0\space g \), and \( m_2>m_1 \).

Step3: Compare heat added

Since \( q \propto m \) (when \( c \) and \( \Delta T \) are constant), the system with larger mass (\( 100.0\space g \) Al) will have more heat added.

Answer:

The heat added is greater for the 100.0 g Al system.