Problemas
3. A 0.240 kg chunk of carbon is heated to 215^circ C and quickly placed into 0 .275 kg of water that has a temperature of 12^circ C What will the final temperature of the water be?
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Silvia
élite · Tutor durante 8 años
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Respuesta
To solve this problem, we can use the principle of conservation of energy, which states that the total energy of an isolated system remains constant.In this case, the carbon chunk and the water are the isolated system. The carbon chunk has a high temperature, while the water has a low temperature. When the carbon chunk is placed into the water, heat will be transferred from the carbon chunk to the water until they reach thermal equilibrium, which means they will have the same temperature.Let's denote the final temperature of the water as T_f.The heat lost by the carbon chunk can be calculated using the formula:Q_c = m_c * c_c * (T_i_c - T_f)where:Q_c is the heat lost by the carbon chunk,m_c is the mass of the carbon chunk,c_c is the specific heat capacity of carbon, andT_i_c is the initial temperature of the carbon chunk.The heat gained by the water can be calculated using the formula:Q_w = m_w * c_w * (T_f - T_i_w)where:Q_w is the heat gained by the water,m_w is the mass of the water,c_w is the specific heat capacity of water, andT_i_w is the initial temperature of the water.Since the heat lost by the carbon chunk is equal to the heat gained by the water, we can set the two equations equal to each other:m_c * c_c * (T_i_c - T_f) = m_w * c_w * (T_f - T_i_w)Now we can plug in the given values and solve for T_f:0.240 kg * 0.71 J/g°C * (215°C - T_f) = 0.275 kg * 4.18 J/g°C * (T_f - 12°C)Solving this equation gives us the final temperature of the water:T_f ≈ 14.6°CTherefore, the final temperature of the water will be approximately 14.6°C.