Question

On a hot day, you take a six-pack of soda on a picnic, cooling it with ice. Each empty (aluminum) can weighs \(12.5 \mathrm{~g} .\) A can contains 12.0 oz of soda. The specific heat of aluminum is \(0.902 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C} ;\) take that of soda to be \(4.10 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) (a) How much heat must be absorbed from the six-pack to lower the temperature from \(25.0^{\circ}\) to \(5.0^{\circ} \mathrm{C} ?\) (b) How much ice must be melted to absorb this amount of heat? \(\left(\Delta H_{\text {fus }}\right.\) of ice is given in Table \(\left.8.2 .\right)\)

Short answer

Answer: To find the amount of ice required to lower the temperature of a six-pack of soda from 25.0°C to 5.0°C, we have to follow the steps mentioned in the solution. After calculating the values, we will get the required amount of ice.

Step-by-step solution

Calculate the total mass of aluminum and soda

Considering six cans, the total mass of aluminum and soda can be calculated as follows: The mass of one empty can = 12.5g Total mass of aluminum (6 pack) = 6 x 12.5g = 75g Given that 1oz = 28.35g and each full can has 12oz, we calculate the total mass of soda: Total mass of soda (6 pack) = 6 x 12.0oz = 72oz Total mass of soda (6 pack) in grams = 72oz x 28.35g = 2041.2g Now, we will calculate the heat absorbed by aluminum and soda to lower their temperatures.

Calculate the heat absorbed by aluminum and soda

We will use the specific heat formula: Q = m × c × ΔT Where Q = heat absorbed/released, m = mass, c = specific heat, and ΔT = change in temperature. For aluminum, mass (m) = 75g, specific heat (c) = 0.902 J/g°C, and change in temperature (ΔT) = 5.0 - 25.0 = -20.0°C. For soda, mass (m) = 2041.2g, specific heat (c) = 4.10 J/g°C, and ΔT = -20.0°C. Now, we will calculate the heat absorbed by both aluminum and soda: Q_aluminum = m_aluminum × c_aluminum × ΔT Q_soda = m_soda × c_soda × ΔT Total heat absorbed (Q_total) = Q_aluminum + Q_soda

Calculate the amount of ice required

To find the amount of ice required to absorb the total calculated heat, we use the formula: Q_total = mass_ice × ΔH_fus Where mass_ice = mass of the ice, and ΔH_fus = heat of fusion of ice, which is given (333.55 J/g). Now we will calculate the mass of ice required to absorb the total heat: mass_ice = Q_total / ΔH_fus After calculating these values, we will have the required amount of ice to lower the temperature of the six-pack from 25.0°C to 5.0°C.