Question

2. A 250.0 g gold statue at 21.0°C is placed in a tank containing 1105. g of water at an initial temperature

of 80°C. If no heat enters or leaves the system, find the final equilibrium temperature.

Answer 1

The final equilibrium temperature of the system is 37.9°C.

Step-by-step explanation:

To find the final equilibrium temperature, we need to use the principle of heat conservation, which states that the total heat lost by the hot water is equal to the total heat gained by the cold gold statue. We can express this principle mathematically as follows:

Q_lost = Q_gained

where Q_lost is the heat lost by the water, and Q_gained is the heat gained by the gold statue.

To calculate the heat lost by the water, we can use the formula:

Q_lost = m_w * c_w * (T_i - T_f)

where m_w is the mass of the water, c_w is the specific heat capacity of water, T_i is the initial temperature of the water, and T_f is the final equilibrium temperature.

To calculate the heat gained by the gold statue, we can use the formula:

Q_gained = m_g * c_g * (T_f - T_i)

where m_g is the mass of the gold statue, c_g is the specific heat capacity of gold, T_i is the initial temperature of the gold statue, and T_f is the final equilibrium temperature.

Equating Q_lost and Q_gained, we have:

m_w * c_w * (T_i - T_f) = m_g * c_g * (T_f - T_i)

Substituting the given values, we get:

1105. g * 4.184 J/g°C * (80°C - T_f) = 250.0 g * 0.129 J/g°C * (T_f - 21.0°C)

Simplifying and solving for T_f, we get:

T_f = 37.9°C

Therefore, the final equilibrium temperature is 37.9°C.