(9) [10 points] You are working with a billet of copper 1.0 cm× 1.0 cm in cross section and 12

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(9) [10 points] You are working with a billet of copper \( 1.0 \mathrm{~cm} \times 1.0 \mathrm{~cm} \) in cross section and \( 12.5 \mathrm{~cm} \) in length at room temperature \( 20^{\circ} \mathrm{C} \). You heat it to a red-hot temperature of \( 850^{\circ} \mathrm{C} \) in an oven and then take it out and hang it from a thin insulating fiber. (a) What is the length of the hot billet? (b) How much heat energy was added to the billet? (c) Calculate the rate of energy loss of the cooling billet at \( 850^{\circ} \mathrm{C} \) and at \( 100^{\circ} \mathrm{C} \). Remember to take into account heat energy coming in from the environment at room temperature. Neglect any effects of convection. Red hot bodies have emissivity of 1 . (d) Taking half the \( 850^{\circ} \mathrm{C} \) energy loss rate as an approximate average rate of energy loss, how long does it take to cool? Hint: you are removing the energy found in part (b). Instead of waiting for the above billet to radiate the energy, you drop it into \( 75.0 \mathrm{~g} \) of water at \( 20^{\circ} \mathrm{C} \). You see some water boil away. (e) How much water is left when the billet has reached \( 100^{\circ} \mathrm{C} \) ? Hint: start with the heat energy removed from the billet to reach \( 100^{\circ} \mathrm{C} \), which is somewhat less than you calculated in the previous problem. You can look up any material parameters you need, just write them clearly and separately and cite the source.

          (9) [10 points] You are working with a billet of copper \( 1.0 \mathrm{~cm} \times 1.0 \mathrm{~cm} \) in cross section and \( 12.5 \mathrm{~cm} \) in length at room temperature \( 20^{\circ} \mathrm{C} \). You heat it to a red-hot temperature of \( 850^{\circ} \mathrm{C} \) in an oven and then take it out and hang it from a thin insulating fiber.
(a) What is the length of the hot billet?
(b) How much heat energy was added to the billet?
(c) Calculate the rate of energy loss of the cooling billet at \( 850^{\circ} \mathrm{C} \) and at \( 100^{\circ} \mathrm{C} \). Remember to take into account heat energy coming in from the environment at room temperature. Neglect any effects of convection. Red hot bodies have emissivity of 1 .
(d) Taking half the \( 850^{\circ} \mathrm{C} \) energy loss rate as an approximate average rate of energy loss, how long does it take to cool? Hint: you are removing the energy found in part (b).
Instead of waiting for the above billet to radiate the energy, you drop it into \( 75.0 \mathrm{~g} \) of water at \( 20^{\circ} \mathrm{C} \). You see some water boil away.
(e) How much water is left when the billet has reached \( 100^{\circ} \mathrm{C} \) ? Hint: start with the heat energy removed from the billet to reach \( 100^{\circ} \mathrm{C} \), which is somewhat less than you calculated in the previous problem.
You can look up any material parameters you need, just write them clearly and separately and cite the source.

(9) [10 points] You are working with a billet of copper 1.0 cm× 1.0 cm in cross section and 12.5 cm in length at room temperature 20^∘C. You heat it to a red-hot temperature of 850^∘C in an oven and then take it out and hang it from a thin insulating fiber.
(a) What is the length of the hot billet?
(b) How much heat energy was added to the billet?
(c) Calculate the rate of energy loss of the cooling billet at 850^∘C and at 100^∘C. Remember to take into account heat energy coming in from the environment at room temperature. Neglect any effects of convection. Red hot bodies have emissivity of 1 .
(d) Taking half the 850^∘C energy loss rate as an approximate average rate of energy loss, how long does it take to cool? Hint: you are removing the energy found in part (b).
Instead of waiting for the above billet to radiate the energy, you drop it into 75.0 g of water at 20^∘C. You see some water boil away.
(e) How much water is left when the billet has reached 100^∘C ? Hint: start with the heat energy removed from the billet to reach 100^∘C, which is somewhat less than you calculated in the previous problem.
You can look up any material parameters you need, just write them clearly and separately and cite the source.

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