A piece of lead with a mass of 27.3 g was heated to 98.90^∘ C and then dropped into 15.0 g of wa

step 1 This is solution number 70. So given mass of lead is 27 .3 and specific heat capacity of water,

A piece of lead with a mass of 27.3 g was heated to 98.90^∘...

A piece of lead with a mass of $27.3 \mathrm{g}$ was heated to $98.90^{\circ} \mathrm{C}$ and then dropped into $15.0 \mathrm{g}$ of water at $22.50^{\circ} \mathrm{C} .$ The final temperature was $26.32^{\circ} \mathrm{C} .$ Calculate the specific heat capacity of lead from these data.

Key Concepts

Heat Transfer Equation

The equation Q = m·c·?T is central to calorimetry. Here, Q represents the heat absorbed or released, m is the mass of the substance, c is its specific heat capacity, and ?T is the change in temperature. It provides a quantitative way to relate temperature changes to energy transfer.

Specific Heat Capacity

This is a property of a material that indicates the amount of heat required to raise the temperature of one gram (or unit mass) of the substance by one degree Celsius (or Kelvin). It’s essential in understanding how different materials respond to heat input.

Calorimetry

Calorimetry is the technique used to measure the amount of heat exchanged in a chemical or physical process. It typically involves isolating the system so that the heat lost by one part of the system is gained by another, allowing calculations of specific heat capacities based on temperature changes.

Conservation of Energy

This principle states that energy within a closed system remains constant. In calorimetry experiments, the heat lost by a hotter object must equal the heat gained by a cooler object, assuming no heat is lost to the surroundings.

Thermal Equilibrium

Thermal equilibrium is reached when two or more substances in contact no longer exchange heat, meaning they have all stabilized at the same temperature. This concept is vital in calorimetry since the final equilibrium temperature is used to determine the amounts of heat gained or lost by the substances involved.

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