Ch.7 - Thermochemistry

Problem 65

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Chapter 7, Problem 65

A silver block, initially at 58.5 °C, is submerged into 100.0 g of water at 24.8 °C, in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 26.2 °C. What is the mass of the silver block?

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First, we need to understand that when two substances are mixed, the heat lost by the hot substance is equal to the heat gained by the cold substance. This is based on the law of conservation of energy. In this case, the silver block is losing heat and the water is gaining heat until they reach thermal equilibrium.

Next, we can express the heat lost by the silver and the heat gained by the water using the formula for heat transfer: q = mcΔT, where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. For the silver block, the change in temperature is (58.5 - 26.2) °C and for the water, the change in temperature is (26.2 - 24.8) °C.

Since the heat lost by the silver block is equal to the heat gained by the water, we can set the two heat transfer equations equal to each other: msilver * csilver * (58.5 - 26.2) = mwater * cwater * (26.2 - 24.8), where msilver is the mass of the silver block we're trying to find, csilver is the specific heat capacity of silver (0.235 J/g°C), mwater is the mass of the water (100.0 g), and cwater is the specific heat capacity of water (4.184 J/g°C).

Now, we can solve the equation for msilver. First, we can simplify the equation by multiplying out the terms on both sides. Then, we can divide both sides of the equation by csilver * (58.5 - 26.2) to isolate msilver on one side of the equation.

Finally, we can substitute the known values into the equation to calculate the mass of the silver block. Remember to check your units and make sure they are consistent throughout the calculation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Heat Transfer and Thermal Equilibrium

Heat transfer occurs when two substances at different temperatures come into contact, leading to energy exchange until they reach thermal equilibrium. In this scenario, the silver block loses heat while the water gains heat until both reach the same final temperature, which is crucial for solving the problem.

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. Each material has a unique specific heat capacity, which is essential for calculating the heat gained or lost by the silver block and the water in this thermal exchange.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed. In this context, the heat lost by the silver block equals the heat gained by the water, allowing us to set up an equation to find the mass of the silver block based on the temperatures and specific heat capacities involved.

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Law of Conservation of Mass

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