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A 50 g block of metal is heated to 200^(...

A 50 g block of metal is heated to `200^(@)C` and then dropped into a beaker containing 0.5 kg of water initially at `20^(@)C.` if the final equilibrium temperature of the mixed system is `22.4^(@)C`, find the specific heat capacity of the metal. Given, specific heat capacity of water is 4182 J `kg^(-1).^(@)C^(-1)`.

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To find the specific heat capacity of the metal block, we can follow these steps: ### Step 1: Identify the known values - Mass of the metal block, \( m_{metal} = 50 \, \text{g} = 0.05 \, \text{kg} \) - Initial temperature of the metal block, \( T_{initial, metal} = 200 \, ^\circ C \) - Mass of water, \( m_{water} = 0.5 \, \text{kg} \) - Initial temperature of water, \( T_{initial, water} = 20 \, ^\circ C \) - Final equilibrium temperature, \( T_{final} = 22.4 \, ^\circ C \) ...
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