Question

An aluminum cup contains 225 g of water and a 40-g copper stirrer, all at 27°C. A 450-g sample of silver at an initial temperature of 89°C is placed in the water. The stirrer is used to stir the mixture gently until it reaches its final equilibrium temperature of 32°C. Calculate the mass of the aluminum cup. (in g)

Answer 1

To calculate the mass of the aluminum cup, we can use the principle of conservation of energy. The heat lost by the silver is equal to the heat gained by the water, the copper stirrer, and the aluminum cup. We can 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.

Since the final temperature is lower than the initial temperature, we'll use a negative sign for the heat lost by the silver.

Let's calculate the heat gained by the water and the copper stirrer first:

Q_water = m_water * c_water * ΔT_water
Q_copper = m_copper * c_copper * ΔT_copper

where m_water is the mass of water, c_water is the specific heat capacity of water, ΔT_water is the change in temperature of water, m_copper is the mass of the copper stirrer, c_copper is the specific heat capacity of copper, and ΔT_copper is the change in temperature of the copper stirrer.

Next, let's calculate the heat lost by the silver:

Q_silver = -m_silver * c_silver * ΔT_silver

where m_silver is the mass of the silver, c_silver is the specific heat capacity of silver, and ΔT_silver is the change in temperature of the silver.

Finally, since the heat gained by the water, copper stirrer, and aluminum cup is equal to the heat lost by the silver, we can write:

Q_water + Q_copper + Q_cup = Q_silver

Now we can solve for the mass of the aluminum cup.