Question:

A student is conducting an experiment to determine the specific heat capacity of a metal block. The student places the metal block in boiling water for a while to ensure it reaches the same temperature as the boiling water, and then quickly transfers it to a calorimeter containing a known mass of water at room temperature. The initial temperature of the metal block and boiling water is 100°C, while the initial temperature of the water in the calorimeter is 20°C. The final equilibrium temperature of the system is measured to be 35°C. The specific heat capacity of water is 4.18 J/g°C. Assuming no heat is lost to the surroundings or gained from the surroundings, calculate the specific heat capacity of the metal block.

Answer:

To calculate the specific heat capacity of the metal block, we need to use the principle of conservation of energy. The energy lost by the metal block must be gained by the water in the calorimeter.

The heat lost by the metal block can be calculated using the formula:

Q_loss = m_block * c_block * (T_final - T_initial)

Where:

• Q_loss is the heat lost by the metal block,
• m_block is the mass of the metal block,
• c_block is the specific heat capacity of the metal block,
• T_final is the final equilibrium temperature of the system,
• T_initial is the initial temperature of the metal block and boiling water.

The heat gained by the water can be calculated using the formula:

Q_gain = m_water * c_water * (T_final - T_initial)

Where:

• Q_gain is the heat gained by the water,
• m_water is the mass of the water in the calorimeter,
• c_water is the specific heat capacity of water,
• T_final is the final equilibrium temperature of the system,
• T_initial is the initial temperature of the water in the calorimeter.

Since no heat is lost or gained to the surroundings, we can set the heat lost by the metal block equal to the heat gained by the water:

m_block * c_block * (T_final - T_initial) = m_water * c_water * (T_final - T_initial)

Now we can solve for the specific heat capacity of the metal block, c_block:

c_block = (m_water * c_water * (T_final - T_initial)) / (m_block * (T_final - T_initial))

Given:

• m_water = mass of water in the calorimeter = known value
• c_water = specific heat capacity of water = 4.18 J/g°C
• T_final = final equilibrium temperature = 35°C
• T_initial = initial temperature of metal block and boiling water = 100°C

Plugging in the known values:

c_block = (m_water * c_water * (T_final - T_initial)) / (m_block * (T_final - T_initial))

c_block = (m_water * 4.18 * (35 - 100)) / (m_block * (35 - 100))

Since we are assuming a known mass of water in the calorimeter and no heat loss or gain to the surroundings, we can simplify the equation further:

c_block = (m_water * 4.18 * (35 - 100)) / (m_block * (35 - 100))

c_block = m_water * 4.18 / m_block

So, the specific heat capacity of the metal block is given by:

c_block = m_water * 4.18 / m_block