DATA 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°C and the other end in thermal contact with an ice–water mixture at 0.0°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°C. After 10 minutes you repeal 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.
DATA 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°C and the other end in thermal contact with an ice–water mixture at 0.0°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°C. After 10 minutes you repeal 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.
DATA 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 cm2. You place one end of bar A in thermal contact with a very large vat of boiling water at 100.0°C and the other end in thermal contact with an ice–water mixture at 0.0°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 kA 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°C. After 10 minutes you repeal 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.
An aluminum bar has a cross-section that is 4.31 cm by 7.32 cm and is 2.38 m long. Aluminum has a thermal conductivity of 205 W/m K. If the aluminum bar is used to bridge between ice at 0 °C
and boiling water at 100 °C, what is the rate of heat transfer (in W) along the bar?
A copper bar is welded end to end to a bar of an unknown metal. The two bars have the same lengths and cross-sectional areas. The free end of the copper bar is maintained at a temperature TH that can be varied. The free end of the unknown metal is kept at 0.0∘C. To measure the thermal conductivity of the unknown metal, you measure the temperature T at the junction between the two bars for several values of TH. You plot your data as T versus TH both in kelvins, and find that your data are well fit by a straight line that has slope 0.460.
What do your measurements give for the value of the thermal conductivity of the unknown metal? Use kCu = 385 W/(m⋅K) .
A rod made of glass has a circular cross section with a diameter of 0.1200 m at a temperature of 20 degrees celsius. An aluminum ring has a diameter of 0.1196 m at a temperature of 20 degrees celsius. The
coefficients of thermal expansion for glass and aluminum are 9.0 x 10-6 1/K and 24.0 x 10-6 1/K, respectively.
At what temperature will the aluminum ring be able to slip over the glass rod?
Between 225 and 250 degrees celsius
Between 175 and 200 degrees celsius
Between 100 and 125 degrees celsius
Higher than 300 degrees celsius
Between 250 and 275 degrees celsius
Between 125 and 150 degrees celsius
Between 275 and 300 degrees celsius
Between 150 and 200 degrees celsius
O Between 200 and 225 degrees celsius
Chapter 17 Solutions
University Physics with Modern Physics Plus Mastering Physics with eText -- Access Card Package (14th Edition)
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