This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
You're on a roll — This is a calorimetry problem where heat lost by the hot water is equal to the heat gained by the cold water, assuming no heat loss to the surroundings or the container. Step 1: Identify the given values and the unknown. Mass of cold water, m_c = 6 kg Initial temperature of cold water, T_ci = 25^ Final temperature of the mixture, T_f = 60^ Initial temperature of boiled water (hot water), T_hi = 100^ (assuming boiled water is at its boiling point). Specific heat capacity of water, c (will cancel out). Mass of hot water, m_h = ? (this is what we need to find). Step 2: Calculate the change in temperature for both the cold and hot water. Change in temperature for cold water: T_c = T_f - T_ci = 60^ - 25^ = 35^ Change in temperature for hot water: T_h = T_hi - T_f = 100^ - 60^ = 40^ Step 3: Apply the principle of calorimetry: Heat lost by hot water = Heat gained by cold water. The formula for heat transfer is Q = mc T. Q_h = Q_c m_h c T_h = m_c c T_c Since the specific heat capacity of water (c) is the same for both, it cancels out: m_h T_h = m_c T_c Step 4: Substitute the values and solve for m_h. m_h (40^) = (6 kg) (35^) m_h = (6 kg) (35^)40^ m_h = (210)/(40) kg m_h = 5.25 kg Step 5: Compare the calculated mass with the given options. The calculated mass is 5.25 kg. Among the options, 5 kg is the closest value. The correct option is B) 5kg. Last one for today! Hope it helped.