A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at 25.1°C A 121.0-g block of copper metal is heated to 100.4°C by putting it in a beaker of boiling water. The specific heat of Cu(s) is 0.385 J/g-K The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of 30.1°C. (a) Determine the amount of heat, in J, lost by the copper block.

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Identify the initial and final temperatures of the copper block: \(T_{\text{initial, Cu}} = 100.4^\circ\text{C}\) and \(T_{\text{final, Cu}} = 30.1^\circ\text{C}\).

Calculate the change in temperature for the copper block: \(\Delta T_{\text{Cu}} = T_{\text{final, Cu}} - T_{\text{initial, Cu}}\).

Use the formula for heat transfer: \(q = m \cdot c \cdot \Delta T\), where \(m\) is the mass of the copper block, \(c\) is the specific heat capacity of copper, and \(\Delta T\) is the change in temperature.

Substitute the known values into the formula: \(m = 121.0\, \text{g}\), \(c = 0.385\, \text{J/g-K}\), and \(\Delta T\) calculated in step 2.

Calculate the heat lost by the copper block, \(q\), using the substituted values.

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Key Concepts

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

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin). It is a material-specific property that varies between different substances. In this problem, the specific heat of copper is given as 0.385 J/g-K, which will be used to calculate the heat lost by the copper block as it cools down.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. In this scenario, the copper block loses heat to the water in the calorimeter until thermal equilibrium is reached. The principle of conservation of energy dictates that the heat lost by the copper will equal the heat gained by the water.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this context, a coffee-cup calorimeter is used to measure the heat exchange between the copper block and the water. By applying the formula Q = mcΔT, where Q is heat, m is mass, c is specific heat, and ΔT is the change in temperature, we can determine the heat lost by the copper.

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Textbook Question

A house is designed to have passive solar energy features. Brickwork incorporated into the interior of the house acts as a heat absorber. Each brick weighs approximately 1.8 kg. The specific heat of the brick is 0.85 J/g•K. How many bricks must be incorporated into the interior of the house to provide the same total heat capacity as 1.7⨉10³ gal of water?

Textbook Question

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at 25.1°C A 121.0-g block of copper metal is heated to 100.4°C by putting it in a beaker of boiling water. The specific heat of Cu(s) is 0.385 J/g-K The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of 30.1°C (b) Determine the amount of heat gained by the water. The specific heat of water is 4.184 J/1gK.

Textbook Question

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at 25.1°C A 121.0-g block of copper metal is heated to 100.4°C by putting it in a beaker of boiling water. The specific heat of Cu(s) is 0.385 J/g-K The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of 30.1°C (d) What would be the final temperature of the system if all the heat lost by the copper block were absorbed by the water in the calorimeter?

Textbook Question

(b) Assuming that there is an uncertainty of 0.002 °C in each temperature reading and that the masses of samples are measured to 0.001 g, what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?