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Chapter 14: Problem 18

What is the heat capacity of a system consisting of (a) a \(0.450-\mathrm{kg}\) brass cup filled with \(0.050 \mathrm{kg}\) of water? (b) \(7.5 \mathrm{kg}\) of water in a 0.75 -kg aluminum bucket?

Short Answer

Expert verified
Answer: The heat capacities of the systems are (a) 382.55 J/K (brass cup filled with water) and (b) 32089.50 J/K (aluminum bucket filled with water).

Step by step solution

01

Identify known quantities and specific heat capacities

We are given the masses and the materials of the objects: (a) Brass cup mass = 0.450 kg, Water mass = 0.050 kg (b) Aluminum bucket mass = 0.75 kg, Water mass = 7.5 kg We also need the specific heat capacities of the materials: Specific heat capacity for brass = \(385\mathrm{ \frac{J}{kg \cdot K}}\) (from reference) Specific heat capacity for water = \(4186\mathrm{ \frac{J}{kg \cdot K}}\) (from reference) Specific heat capacity for aluminum = \(900\mathrm{ \frac{J}{kg \cdot K}}\) (from reference)
02

Calculate the heat capacity of each component

We'll use the formula heat capacity = mass 脳 specific heat capacity for each component: For (a): Heat capacity of brass cup: \(0.450\mathrm{kg}\times385\mathrm{ \frac{J}{kg \cdot K}} = 173.25\mathrm{J/K}\) Heat capacity of water in the brass cup: \(0.050\mathrm{kg}\times4186\mathrm{ \frac{J}{kg \cdot K}} = 209.30\mathrm{J/K}\) For (b): Heat capacity of aluminum bucket: \(0.75\mathrm{kg}\times 900\mathrm{ \frac{J}{kg \cdot K}} = 675\mathrm{J/K}\) Heat capacity of water in the aluminum bucket: \(7.5\mathrm{kg}\times 4186\mathrm{ \frac{J}{kg \cdot K}} = 31414.50\mathrm{J/K}\)
03

Calculate the heat capacity of the whole system

Now, we'll find the heat capacity for the entire system by adding the heat capacities of the individual components: For (a): Total heat capacity of the brass cup with water: \(173.25\mathrm{J/K} + 209.30\mathrm{J/K} = 382.55\mathrm{J/K}\) For (b): Total heat capacity of the aluminum bucket with water: \(675\mathrm{J/K} + 31414.50\mathrm{J/K} = 32089.50\mathrm{J/K}\) So, the heat capacities of the systems are: (a) \(382.55\mathrm{J/K}\) (brass cup filled with water) (b) \(32089.50\mathrm{J/K}\) (aluminum bucket filled with water)

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Most popular questions from this chapter

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