A person pours 330 g of water at 55°C into an 855-g aluminum container with an initial temperature of 10°C. The specific heat of aluminum is

Question

A person pours 330 g of water at 55°C into an 855-g aluminum container with an initial temperature of 10°C. The specific heat of aluminum is 900 J/(kg・ΕK) and that of water is 4190 J/(kg・ΕK). What is the final temperature of the system, assuming no heat is exchanged with the surroundings?

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Thiên Thanh 5 months 2021-08-09T15:42:52+00:00 1 Answers 39 views 0

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    2021-08-09T15:43:58+00:00

    Answer:

    The final temperature of the system is 39⁰C

    Explanation:

    Applying principle of conservation of heat energy;

    Heat loss by a hot body = heat gained by a cold body

    m_hc(T_i_h -T) = m_c(T-T_i_c)

    where;

    Mh is the mass of the hot fluid = 330 g = 0.33 kg

    Mc  is the mass of the cold fluid = 855-g = 0.855 kg

    Tih is the initial temperature of the hot fluid = 55°C

    Tic is the initial temperature of the cold fluid = 10°C

    T is the final temperature of the mixture

    Substitute the given values and solve for T

    m_hc(T_i_h -T) = m_c(T-T_i_c)\\\\0.33*4190(55 -T) = 0.855*900(T-10)\\\\1382.7(55 -T) = 769.5(T-10)\\\\(T-10) = 1.797(55 -T)\\\\T-10 = 98.835 -  1.797T\\\\T+  1.797T = 98.835 + 10\\\\2.797T= 108.835\\\\T = \frac{108.835}{2.797}  = 39^o C

    Therefore, the final temperature of the system is 39⁰C

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