550 g of water (cw = 4186 J/kg.K) at 75°C is poured into an 855 g aluminum (cw =900 J/kg.K) container with an initial temperature of 11°C. What is the final temperature of the system, assuming no heat is exchanged with the surroundings?

Select one:
a. 75 °C
b. 59 °C
c. 11 °C
d. 64 °C

b.59

What is the final temperature of the system, assuming no heat is exchanged with the

Why did the water go to the therapist? Because it had a lot of emotional heat!

Now, to answer your question, let's calculate the amount of heat gained by the water and the amount of heat lost by the aluminum container.

For the water, we can use the formula:
Qwater = mcwΔT
where m is the mass of the water, cw is the specific heat capacity of water, and ΔT is the change in temperature.

For the aluminum container, we can use the formula:
Qaluminum = maluminumcwΔT
where ma is the mass of the aluminum container and cw is the specific heat capacity of aluminum.

Since no heat is exchanged with the surroundings, the amount of heat gained by the water is equal to the amount of heat lost by the aluminum container, so:
Qwater = Qaluminum

Now, let's plug in the values:
550g x 4186J/kg.K x (Tfinal - 75°C) = 855g x 900J/kg.K x (11°C - Tfinal)

Solving this equation gives us Tfinal ≈ 59°C. So, the final temperature of the system is approximately 59 °C.

Therefore, the correct answer is b. 59 °C.

To find the final temperature of the system, we can use the principle of conservation of energy. The total heat gained by the water and the container is equal to the total heat lost by the water and the container.

The heat gained by the water can be calculated using the formula:

Q_water = m_water * cw * (T_final - T_initial)

Where:
Q_water is the heat gained by the water,
m_water is the mass of the water (550 g),
cw is the specific heat capacity of water (4186 J/kg.K),
T_final is the final temperature of the system,
T_initial is the initial temperature of the water (75 °C).

Similarly, the heat gained by the container can be calculated using the formula:

Q_container = m_container * cw * (T_final - T_initial)

Where:
Q_container is the heat gained by the container,
m_container is the mass of the container (855 g),
cw is the specific heat capacity of aluminum (900 J/kg.K),
T_final is the final temperature of the system,
T_initial is the initial temperature of the container (11 °C).

Since no heat is exchanged with the surroundings, the heat gained by the water and the container should equal zero:

Q_water + Q_container = 0

Substituting the formulas for Q_water and Q_container:

m_water * cw * (T_final - T_initial) + m_container * cw * (T_final - T_initial) = 0

Simplifying the equation:

550 * 4186 * (T_final - 75) + 855 * 900 * (T_final - 11) = 0

Now, we can solve this equation to find the value of T_final. By solving the equation, we get:

3,939,850 * T_final - 268,012,700 = 0

T_final = 268,012,700 / 3,939,850

T_final = 67.96 °C

So, the final temperature of the system is approximately 68 °C.

None of the given options match the calculated value, so the answer is not among the choices provided.

550 g of water (cw = 4186 J/kg.K) at 75°C is poured into an 855 g aluminum (cw =900 J/kg.K) container with an initial temperature of 11°C. What is the final temperature of the system, assuming no heat is exchanged with the surroundings?

D. 64