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?

Answer 1

The final temperature of the system is 39⁰C

Step-by-step 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 = (108.835)/(2.797) = 39^o C`

Therefore, the final temperature of the system is 39⁰C