A metal block of iron with a mass of 9.10 g is at 73.6°C. It is added to 99.3 g of water at 13.9°C. What is the final temperature of the block and the water?

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

The equation to calculate the heat transfer is:

Q = mcΔT

Where:

Q is the heat transfer (in joules)
m is the mass (in kg)
c is the specific heat capacity (in J/g°C or J/kg°C)
ΔT is the change in temperature (in °C)

For the iron block, the mass (m) is 9.10 g and the specific heat capacity (c) is 0.449 J/g°C. The change in temperature (ΔT) is the final temperature (T_f) minus the initial temperature (Ti).

For the water, the mass (m) is 99.3 g and the specific heat capacity (c) is 4.18 J/g°C. The change in temperature (ΔT) is the final temperature (T_f) minus the initial temperature (Ti).

Using the equation and the given values, we can set up the following equation:

(9.10 g)(0.449 J/g°C)(T_f - 73.6°C) = (99.3 g)(4.18 J/g°C)(T_f - 13.9°C)

Simplifying the equation, we get:

4.0989 T_f - 2990.84 = 414.174 T_f - 5771.542

4.0989 T_f - 414.174 T_f = -5771.542 + 2990.84

-410.0751 T_f = -2777.702

T_f ≈ 6.77°C

Therefore, the final temperature of the block and the water is approximately 6.77°C.

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