At a chemical plant where you are an engineer, a tank...

At a chemical plant where you are an engineer, a tank contains an unknown liquid. You must determine the liquid's specific heat capacity. You put $0.500 \mathrm{~kg}$ of the liquid into an insulated metal cup of mass $0.200 \mathrm{~kg}$. Initially the liquid and cup are at $20.0^{\circ} \mathrm{C}$. You add $0.500 \mathrm{~kg}$ of water that has a temperature of $80.0^{\circ} \mathrm{C}$. After thermal equilibrium has been reached, the final temperature of the two liquids and the cup is $58.1^{\circ} \mathrm{C}$. You then empty the cup and repeat the experiment with the same initial temperatures, but this time with $1.00 \mathrm{~kg}$ of the unknown liquid. The final temperature is $49.3^{\circ} \mathrm{C}$. Assume that the specific heat capacities are constant over the temperature range of the experiment and that no heat is lost to the surroundings. Calculate the specific heat capacity of the liquid and of the metal from which the cup is made.

Key Concepts

Conservation of Energy

This principle states that energy can neither be created nor destroyed, only transferred or converted from one form to another. In thermal processes, such as mixing substances at different temperatures, the heat lost by the hotter materials must equal the heat gained by the cooler ones in an insulated system.

Calorimetry

Calorimetry is the experimental technique used to measure the heat exchanged in chemical or physical processes. It involves isolating a system to prevent heat loss or gain from the surroundings and determining the specific heat capacity of materials by observing temperature changes resulting from heat transfer.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one kilogram of a substance by one degree Celsius (or Kelvin). This intrinsic property plays a crucial role in determining how substances respond to heat and is calculated using a relation between the mass, temperature change, and the heat absorbed or released.

Thermal Equilibrium

Thermal equilibrium occurs when two or more substances reach a common temperature after exchanging heat. This concept is essential in calorimetry because, at equilibrium, the final temperature provides a basis for equating the heat lost by the warmer substances to the heat gained by the cooler ones.

Heat Transfer Equation

The heat transfer equation, typically expressed as Q = m × c × ?T, quantifies the amount of heat (Q) transferred to or from a substance, where m is the mass, c is the specific heat capacity, and ?T is the change in temperature. This expression is fundamental in setting up equations to solve for unknown thermal properties during calorimetric experiments.

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