A 25 g gold nugget with an initial temperature of 60 °C is dropped into an insulated cup containing 100 ml of water initially at a temperature of 5°C. What is the final temperature after thermal equilibrium is established? Refer to Table 3.4 of the text for information on specific heats of these substances.

I am not going to Google them for you

1 mL of water is about 1 gram of water

SHgold*25 (60-T) = SHwater * 100 grams * (T-5)

To find the final temperature after thermal equilibrium is established, we need to use the concept of heat transfer and the specific heat capacities of gold and water.

First, let's gather the necessary information from Table 3.4. The specific heat capacity of gold is 0.13 J/g°C, and the specific heat capacity of water is 4.18 J/g°C.

1. Calculate the heat transferred from the gold nugget to the water:
To do this, we use the formula: Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

The heat transferred from the gold nugget to the water can be calculated as:
Q = (mass of gold nugget) x (specific heat capacity of gold) x (change in temperature of gold nugget)
Q = 25 g x 0.13 J/g°C x (final temperature - initial temperature of gold nugget)

2. Calculate the heat absorbed by the water:
Similarly, we calculate the heat absorbed by the water using the same formula:
Q = (mass of water) x (specific heat capacity of water) x (change in temperature of water)
Q = 100 g (since the density of water is 1 g/mL) x 4.18 J/g°C x (final temperature - initial temperature of water)

Both equations equal the same heat transfer value because the heat lost by the gold nugget is equal to the heat gained by the water.

3. Equate the two equations and solve for the final temperature:
Set the equations equal to each other:
25 g x 0.13 J/g°C x (final temperature - 60°C) = 100 g x 4.18 J/g°C x (final temperature - 5°C)

Simplify the equation:
3.25 J/°C x (final temperature - 60°C) = 418 J/°C x (final temperature - 5°C)

Distribute and rearrange to isolate the final temperature term:
(3.25 J/°C) x (final temperature) - (3.25 J/°C) x (60°C) = (418 J/°C) x (final temperature) - (418 J/°C) x (5°C)

Combine like terms:
(3.25 J/°C - 418 J/°C) x (final temperature) = (3.25 J/°C x 60°C) - (418 J/°C x 5°C)

Solve for the final temperature:
(final temperature) = [(3.25 J/°C x 60°C) - (418 J/°C x 5°C)] / (3.25 J/°C - 418 J/°C)

Calculate the final temperature using this equation.

Note: Remember to perform the operations in brackets first, then divide to get the final temperature.