1) An aluminum cup with a cylindrical shape contains 403.0 grams of ethyl alcoho
ID: 1583917 • Letter: 1
Question
1) An aluminum cup with a cylindrical shape contains 403.0 grams of ethyl alcohol with a volume of 500.0 cm both of which are initially at room temperature of 20.00 °C. The aluminum cup has a mass of 150.0 grams, and an inside radius of 4.000 cm. A 672.0 gram silver cube has a length of 4.000 cm on a side at its initial temperature of 95.00 °C. The silver cube is then placed in the aluminum cup containing the ethyl alcohol. Use this information to answer the following questions. What is the specific heat of the silver if the mixture reaches an equilibrium temperature Of 29.30°C. a) [10 points] What is the initial (inner) height of the cup, if the cup is completely full when the mixture reaches the equilibrium temperature? [10 points] b) If the experiment was done without thermally isolating the cup would the value for the specific heat in part (a) be higher, lower, or the same? Explain your answer fully, or show proof. [5 points c)Explanation / Answer
specific heat of ethyl alcohol = 2.46 J/g °C
let specific heat of silver = S J/g °C
mass of ethyl alcohol = 403 gram and container is thermally isolated
mass of silver cube = 672 gram
initial temperature of mixture = 20 °C
initial temperature of silver cube = 95 °C
final temperature = 29.3 °C
temperature diff in silver cube = 65.7 °C loss
temperature gain in mixture = 9.3 °C gain
energy released by silver cube = energy gained by mixture = 2.46 * 403 * 9.3 = S * 672 * 65.7
=> S = 0.208 J/g °C
a) specific heat of silver = 0.208 J/g °C
b) initial volume of cup = volume of methyl alcohol + volume of silver cube = pi * r^2*h
=> h = (volume of methyl alcohol + volume of silver cube)/( pi * r^2) = 11.22 cm
c) if the experiment was done without thermally isolating and final temperature is same this implies that heat is not just transferred to mixture but also to the cup.
=> heat released from silver cube = energy gained by mixture + energy gained by cup
=> heat released from silver cube > heat released from silver cube in previous case (assuming final temperture was same)
=> Specific Heat will be more
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