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Ch 19: Work, Heat, and the First Law of Thermodynamics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 19, Problema 43

512 g of an unknown metal at a temperature of 15°C is dropped into a 100 g aluminum container holding 325 g of water at 98°C. A short time later, the container of water and metal stabilizes at a new temperature of 78°C. Identify the metal.

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Determine the heat gained or lost by each component (metal, water, and aluminum container) using the formula for heat transfer: Q = mc∆T, where Q is the heat, m is the mass, c is the specific heat capacity, and ∆T is the change in temperature.
Write the heat transfer equation for the system. Since the system is isolated, the heat lost by the water and aluminum container equals the heat gained by the unknown metal: -(Qwater + Qaluminum) = Qmetal.
Substitute the known values into the heat transfer formula for each component. For water: Qwater = mwatercwater(Tfinal - Tinitial). For aluminum: Qaluminum = maluminumcaluminum(Tfinal - Tinitial). For the metal: Qmetal = mmetalcmetal(Tfinal - Tinitial).
Rearrange the equation to solve for the specific heat capacity of the unknown metal, cmetal. Use the relationship: cmetal = rac{- (Qwater + Qaluminum)}{mmetal(Tfinal - Tinitial)}.
Compare the calculated specific heat capacity of the unknown metal to a table of known specific heat capacities to identify the metal.

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Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a crucial property in thermal energy calculations, as different materials absorb and release heat at different rates. In this problem, knowing the specific heat capacities of aluminum, water, and the unknown metal allows us to set up equations to find the metal's identity based on the heat transfer involved.
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Specific Heat & Temperature Changes

Heat Transfer and Equilibrium

Heat transfer occurs when thermal energy moves from a hotter object to a cooler one until thermal equilibrium is reached, meaning they stabilize at the same temperature. In this scenario, the heat lost by the water and aluminum container equals the heat gained by the unknown metal. This principle is essential for solving the problem, as it allows us to apply the conservation of energy to find the specific heat of the metal.
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Overview of Heat Transfer

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes, as well as heat capacity. In this context, it involves calculating the heat exchanged between the metal, water, and aluminum container to determine the unknown metal's specific heat. By using the formula Q = mcΔT, where Q is heat, m is mass, c is specific heat, and ΔT is the change in temperature, we can derive the necessary equations to identify the metal.
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Solving Calorimetry Problems
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