a 100g cube of aluminium orginally at 120degree celcius is placed into an insulated container of water originally at 18 degree celcius after some time the system reaches equilibrium and the final temperatuee of the water is 22 degree celcius what is the finasl temperatureof the aluminium cube

To determine the final temperature of the aluminum cube, we can apply the principle of conservation of energy, which states that the heat lost by the aluminum will equal the heat gained by the water. Since the system is insulated, no heat is lost to the surroundings. Let's break this down step by step.

Understanding the Heat Transfer

When the aluminum cube is placed in the water, it will lose heat as it cools down, while the water will gain heat as it warms up. The specific heat capacity of aluminum and water will play a crucial role in this calculation.

Key Information

• Mass of aluminum (m_Al) = 100 g = 0.1 kg
• Initial temperature of aluminum (T_{initial, Al}) = 120 °C
• Final temperature of the system (T_final) = 22 °C
• Specific heat capacity of aluminum (c_Al) = 900 J/(kg·°C)
• Mass of water (m_water) = unknown, but we can assume it’s sufficient to reach equilibrium
• Initial temperature of water (T_{initial, water}) = 18 °C
• Specific heat capacity of water (c_water) = 4186 J/(kg·°C)

Applying the Heat Transfer Formula

The formula for heat transfer is given by:

Q = mcΔT

Where:

• Q = heat transferred
• m = mass
• c = specific heat capacity
• ΔT = change in temperature (final temperature - initial temperature)

Calculating Heat Lost by Aluminum

For the aluminum cube, the heat lost (Q_Al) can be calculated as follows:

Q_Al = m_Al × c_Al × (T_final - T_{initial, Al})

Substituting the values:

Q_Al = 0.1 kg × 900 J/(kg·°C) × (22 °C - 120 °C)

Q_Al = 0.1 × 900 × (-98)

Q_Al = -8820 J

Calculating Heat Gained by Water

For the water, the heat gained (Q_water) can be expressed as:

Q_water = m_water × c_water × (T_final - T_{initial, water})

Since we don't know the mass of water, we can denote it as m_water. The equation becomes:

Q_water = m_water × 4186 J/(kg·°C) × (22 °C - 18 °C)

Q_water = m_water × 4186 × 4

Q_water = m_water × 16744 J

Setting Up the Equation

According to the conservation of energy, the heat lost by aluminum equals the heat gained by water:

-Q_Al = Q_water

Substituting the values we calculated:

8820 J = m_water × 16744 J

Finding the Mass of Water

To find the mass of the water, we rearrange the equation:

m_water = 8820 J / 16744 J/kg

m_water ≈ 0.526 kg

Final Temperature of the Aluminum Cube

Since we know the final temperature of the system is 22 °C, this is also the final temperature of the aluminum cube. The aluminum cube reaches thermal equilibrium with the water, meaning they both stabilize at the same temperature.

In summary, the final temperature of the aluminum cube is 22 °C, the same as the final temperature of the water after they have exchanged heat in the insulated container.