Ice chest You are in charge of keeping the drinks cold for a picnic. You have a Styrofoam box that is filled with bottles of cola and you plan to put some 0° C ice in it. Your task is to buy enough ice to put in the box at 6am so that the temperature stays at 0° C until the picnic starts at 6pm. You don't want to buy too much ice because that means that you'll have less money to spend on food and other picnic items. You plan on keeping cold eight 2-liter bottles of cola. How much ice will you need? Today will be beautifully sunny: a perfect day for a picnic. The temperature will start out at 12°C at 6am and then the temperature will steadily increase, reaching 35°C at 6pm. It will be partially cloudy with a mild breeze from the west. Use the following hints and parameters to solve the problem: • Your cubical Styrofoam chest has sides each 0.4 m and thickness of 2 cm. • Heat entering through each of the six sides of the chest is the same. • Neglect the thermal conductivity and heat capacity of the cola containers • The initial temperature of the cola: 20 °C. • The specific heat capacity is the same for cola and water: C_cola = C_water = 4190 J / (kg°C) • The thermal conductivity of Styrofoam: k_Styrofoam = 0.027 W / (m°C)
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First, we need to calculate the heat transfer through the Styrofoam box during the 12 hours (from 6 am to 6 pm). The temperature difference between the inside and outside of the box will change throughout the day. We can assume an average temperature difference Show more…
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Adi S.
Supreeta N.
During your mechanical engineering internship, you are given two uniform metal bars $A$ and $B$, which are made from different metals, to determine their thermal conductivities. Measuring the bars, you determine that both have length 40.0 cm and uniform cross-sectional area 2.50 cm$^2$. You place one end of bar $A$ in thermal contact with a very large vat of boiling water at 100.0$^\circ$C and the other end in thermal contact with an ice-water mixture at 0.0$^\circ$C. To prevent heat loss along the bar's sides, you wrap insulation around the bar. You weigh the amount of ice initially and find it to be 300 g. After 45.0 min has elapsed, you weigh the ice again and find that 191 g of ice remains. The ice-water mixture is in an insulated container, so the only heat entering or leaving it is the heat conducted by the metal bar. You are confident that your data will allow you to calculate the thermal conductivity $k_A$ of bar $A$. But this measurement was tedious-you don't want to repeat it for bar $B$. Instead, you glue the bars together end to end, with adhesive that has very large thermal conductivity, to make a composite bar 80.0 m long. You place the free end of A in thermal contact with the boiling water and the free end of $B$ in thermal contact with the ice-water mixture. As in the first measurement, the composite bar is thermally insulated. You go to lunch; when you return, you notice that ice remains in the ice-water mixture. Measuring the temperature at the junction of the two bars, you find that it is 62.4$^\circ$C. After 10 minutes you repeat that measurement and get the same temperature, with ice remaining in the ice-water mixture. From your data, calculate the thermal conductivities of bar $A$ and of bar $B$.
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