## So What's The Answer?

In order to calculate the specific heat of a metal, data from an experiment is needed where heat is exchanged between a metal sample and another object. The heat exchanged is measured in joules and the mass is measured in grams. The change in temperature is represented by ΔT. The specific heat, denoted as C p, is calculated using the equation C p = Q/mΔT where m represents the mass of the substance. The energy added, Q, and the change in temperature, ΔT, are used in the formula. Additionally, there may be two different entities gaining energy in the experiment, the water and the calorimeter, so an adjusted equation must be used. The substance's specific heat capacity, C, can be calculated using the formula C = Q/(m × ΔT) regardless of the mass of the substance used in the experiment.

The specific heat of the metal can be calculated using the principle of the conservation of energy and the formula for the specific heat. Based on the given data, we can solve the equation ( Q_{\text{lost}} = Q_{\text{gained}} ) to find the specific heat ( C ) of the metal:

[ m_{\text{metal}} \times C \times \Delta T_{\text{metal}} = (m_{\text{water}} + m_{\text{lead}}) \times C_{\text{water}} \times \Delta T_{\text{water}} + m_{\text{lead}} \times C_{\text{lead}} \times \Delta T_{\text{lead}} ]

After rearranging the formula and plugging in the given values, the specific heat ( C ) of the metal can be calculated.

Let's perform these calculations:

- ( m_{\text{metal}} = 0.19 , \text{kg} )
- ( \Delta T_{\text{metal}} = (22.2 - 100) , ^\circ \text{C} )
- ( m_{\text{water}} = 0.54 , \text{kg} )
- ( m_{\text{lead}} = 1.9 , \text{kg} )
- ( \Delta T_{\text{water}} = (22.2 - 20.2) , ^\circ \text{C} )
- ( \Delta T_{\text{lead}} = (22.2 - 20.2) , ^\circ \text{C} )

Upon solving this equation, we will obtain the specific heat ( C ) of the metal.

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