An aluminum block of mass MAl=2.0 kg and specific heat CAl=910 J /(kg K) is at an initial temp

step 1 So here we have the thermal energy lost by the aluminum block, equaling the mass of the aluminum

An aluminum block of mass MAl=2.0 kg and specific heat...

An aluminum block of mass $M_{\mathrm{Al}}=2.0 \mathrm{~kg}$ and specific heat $C_{\mathrm{Al}}=910 \mathrm{~J} /(\mathrm{kg} \mathrm{K})$ is at an initial temperature of $1000{ }^{\circ} \mathrm{C}$ and is dropped into a bucket of water. The water has mass $M_{\mathrm{H}_{2} \mathrm{O}}=12 \mathrm{~kg}$ and specific heat $C_{\mathrm{H}_{2} \mathrm{O}}=4190 \mathrm{~J} /(\mathrm{kg} \mathrm{K})$ and is at room temperature $\left(25^{\circ} \mathrm{C}\right) .$ What is the approximate final temperature of the system when it reaches thermal equilibrium? (Neglect heat loss out of the system.) a) $50^{\circ} \mathrm{C}$ b) $60^{\circ} \mathrm{C}$ c) $70^{\circ} \mathrm{C}$ d) $80^{\circ} \mathrm{C}$

An aluminum block of mass $M_{\mathrm{Al}}=2.0 \mathrm{~kg}$ and specific heat $C_{\mathrm{Al}}=910 \mathrm{~J} /(\mathrm{kg} \mathrm{K})$ is at an initial temperature of $1000{ }^{\circ} \mathrm{C}$
and is dropped into a bucket of water. The water has mass $M_{\mathrm{H}_{2} \mathrm{O}}=12 \mathrm{~kg}$ and specific heat $C_{\mathrm{H}_{2} \mathrm{O}}=4190 \mathrm{~J} /(\mathrm{kg} \mathrm{K})$ and
is at room temperature $\left(25^{\circ} \mathrm{C}\right) .$ What is the approximate final temperature of the system when it reaches thermal equilibrium? (Neglect heat loss out of the system.)
a) $50^{\circ} \mathrm{C}$
b) $60^{\circ} \mathrm{C}$
c) $70^{\circ} \mathrm{C}$
d) $80^{\circ} \mathrm{C}$

Key Concepts

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates how much thermal energy is needed to raise the temperature of a unit mass of the substance by one degree. This concept is fundamental in thermodynamics and is used to calculate how temperature changes when heat is added or removed from a material.

Conservation of Energy

The conservation of energy principle states that energy cannot be created or destroyed, only transferred or transformed. In thermal processes, this means that the heat lost by a hot object must equal the heat gained by a cooler one in an isolated system, allowing us to calculate the final equilibrium temperature.

Thermal Equilibrium

Thermal equilibrium occurs when two or more objects in thermal contact reach the same temperature, resulting in no net heat flow between them. This concept is key when predicting the final state of systems where different bodies with varying initial temperatures interact.

Heat Transfer

Heat transfer is the movement of thermal energy from one body or system to another due to a temperature difference. Understanding the mechanisms and calculations involved in heat transfer is essential for solving problems related to temperature changes in different materials.

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