AP Physics 2 Exam Question - Heat Transfer

A 100 kg block of metal initially at a temperature of 20°C is placed in contact with a 200 kg block of metal initially at a temperature of 80°C. The two blocks are perfectly insulated from their surroundings. The specific heat capacity of the metal is 0.5 J/g°C. Assume no heat is lost to the surroundings.

1. Calculate the change in thermal energy of the 100 kg block when it reaches thermal equilibrium with the 200 kg block.
2. Determine the final equilibrium temperature of the system.

Answer:

1. To calculate the change in thermal energy of the 100 kg block, we need to know the specific heat capacity of the metal and the change in temperature.

   The specific heat capacity of the metal is given as 0.5 J/g°C. As the block has a mass of 100 kg, we need to convert the mass to grams:

   Mass of the block = 100 kg = 100,000 g

   The change in temperature is given by:

   Change in temperature = Final temperature - Initial temperature

   Since the blocks reach thermal equilibrium, the final temperature will be the same for both blocks. Therefore, it is equal to the average of the initial temperatures.

   Initial temperature of 100 kg block = 20°C Initial temperature of 200 kg block = 80°C

   Average initial temperature = (20°C + 80°C) / 2 = 50°C

   Change in temperature = (Final temperature) - (50°C)

   Now, we can calculate the change in thermal energy using:

   Change in thermal energy = (Mass) × (Specific heat capacity) × (Change in temperature)

   Change in thermal energy = (100,000 g) × (0.5 J/g°C) × (Final temperature - 50°C)

2. To determine the final equilibrium temperature of the system, we can use the principle of conservation of energy.

   The change in thermal energy of the 100 kg block is equal to the change in thermal energy of the 200 kg block.

   Change in thermal energy of 100 kg block = Change in thermal energy of 200 kg block

   From previous calculations, we know the change in thermal energy of the 100 kg block is:

   (100,000 g) × (0.5 J/g°C) × (Final temperature - 50°C)

   The change in thermal energy of the 200 kg block can be calculated in a similar way:

   Mass of the block = 200 kg = 200,000 g

   Change in thermal energy of 200 kg block = (200,000 g) × (0.5 J/g°C) × (Final temperature - 50°C)

   Since the change in thermal energy is equal for both blocks, we can set up the equation:

   (100,000 g) × (0.5 J/g°C) × (Final temperature - 50°C) = (200,000 g) × (0.5 J/g°C) × (Final temperature - 50°C)

   Simplifying, we get:

   (100,000 g) × (Final temperature - 50°C) = (200,000 g) × (Final temperature - 50°C)

   Dividing both sides by (Final temperature - 50°C):

   100,000 g = 200,000 g

   This equation is false, meaning there is no solution. Therefore, the final equilibrium temperature of the system cannot be determined based on the given information.

Thus, the answer to the first part of the question is: Change in thermal energy = (100,000 g) × (0.5 J/g°C) × (Final temperature - 50°C)

And the answer to the second part of the question is: The final equilibrium temperature of the system cannot be determined.