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anonymous

  • one year ago

A student pours 46.8g of water at 17oC into a beaker containing 111.4g or water at 17oC. The density of water at 17oC is 1.00 g/mL. (a) What is the final mass? (b) What is the final temperature? (c) What is the final density?

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  1. UnkleRhaukus
    • one year ago
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    Add the volumes

  2. anonymous
    • one year ago
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    160g

  3. UnkleRhaukus
    • one year ago
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    158.2 g

  4. UnkleRhaukus
    • one year ago
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    We can remember that density \(\rho = m/V\) Solve this equation for the mass \(m\), then plug in the values for \(\varrho\), and \(V\)

  5. anonymous
    • one year ago
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    So 160 * 1.00?

  6. UnkleRhaukus
    • one year ago
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    yes

  7. anonymous
    • one year ago
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    so 160 g

  8. UnkleRhaukus
    • one year ago
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    yes 158.2 g

  9. UnkleRhaukus
    • one year ago
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    NB ( 1 cm^3 = 1 ml )

  10. anonymous
    • one year ago
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    what does the NB stand for?

  11. UnkleRhaukus
    • one year ago
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    note well: \( 1\,[\text{cm}^3] = 1\,[\text{mL}]\))

  12. UnkleRhaukus
    • one year ago
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  13. anonymous
    • one year ago
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    Oh. Thanks.

  14. UnkleRhaukus
    • one year ago
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    OK, so you have (a), what do you think about (b)?

  15. anonymous
    • one year ago
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    would temperatures need to be added?

  16. UnkleRhaukus
    • one year ago
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    is temperature an extensive quantity, or intensive ?

  17. anonymous
    • one year ago
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    intensive

  18. UnkleRhaukus
    • one year ago
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    right, so the temperature should become the average

  19. UnkleRhaukus
    • one year ago
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    (not the sum)

  20. UnkleRhaukus
    • one year ago
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    what is the average of 17°C and 17°C ?

  21. anonymous
    • one year ago
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    17

  22. UnkleRhaukus
    • one year ago
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    * is suppose it really should be the weighted average, but yes the temperatures are the same so the temperature wont change

  23. UnkleRhaukus
    • one year ago
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    makes sense?

  24. anonymous
    • one year ago
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    not exactly

  25. UnkleRhaukus
    • one year ago
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    which bits are unclear?

  26. anonymous
    • one year ago
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    how I am suppose to use the average to figure out the final temperature

  27. UnkleRhaukus
    • one year ago
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    i don't think you are expected calculate the temperature, the temperatures are the same

  28. anonymous
    • one year ago
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    so it would be 17 as the final?

  29. UnkleRhaukus
    • one year ago
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    yeah, if you mix so water that is 17°C, with some more water that is 17°C, the temperature of the mixture will be 17°

  30. anonymous
    • one year ago
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    Alright. That makes sense now.

  31. anonymous
    • one year ago
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    Thanks.

  32. UnkleRhaukus
    • one year ago
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    If they were different temperatures, then the final temperature would be some in-between

  33. anonymous
    • one year ago
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    Gotcha. It makes sense now.

  34. UnkleRhaukus
    • one year ago
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    so what do you got for (c) ?

  35. anonymous
    • one year ago
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    You would multiple the final mass by the density to get volume.

  36. anonymous
    • one year ago
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    which gives 160

  37. anonymous
    • one year ago
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    So 160/160 = 1.00g/mL

  38. UnkleRhaukus
    • one year ago
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    (c) is asking for the final density, we know that density (like temperature, but unlike mass) is an intensive quality, i.e. density is a property of the material, rather than the object

  39. UnkleRhaukus
    • one year ago
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    the question states The density of water at 17°C is 1.00 [g/mL]. We found the final temperature of the mixture to be 17°C.

  40. UnkleRhaukus
    • one year ago
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    you don't have you multiply or divide to get (c),

  41. anonymous
    • one year ago
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    why would we need to know the temperature for the final density?

  42. UnkleRhaukus
    • one year ago
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    because the density of water is temperature dependent

  43. anonymous
    • one year ago
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    Okay. Because of the intensive and extensive

  44. anonymous
    • one year ago
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    So you only have to look at it? Not do any math?

  45. UnkleRhaukus
    • one year ago
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    right , there is no math for (c), it is just: notice that our final temperature 17°C, is one at which we know the density to be 1 [g/mL]

  46. anonymous
    • one year ago
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    what makes you realize that?

  47. UnkleRhaukus
    • one year ago
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    it's given in the question

  48. UnkleRhaukus
    • one year ago
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    we found the final temperature in (b), and the question tell us the density of water at this temperature

  49. anonymous
    • one year ago
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    Yeah.

  50. UnkleRhaukus
    • one year ago
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    if the temperatures were different, and we calculated a weighted average temperature, we might use a table to look up the density of water at the temperature

  51. UnkleRhaukus
    • one year ago
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    We are combining objects with the same intensive properties, whereas, the extensive property (the mass) is the sum the intensive properties (temperature and density) of the mixture will be equal.

  52. anonymous
    • one year ago
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    because intensive is independent?

  53. UnkleRhaukus
    • one year ago
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    Yes, intensive properties are independent of the amount we have

  54. anonymous
    • one year ago
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    That makes sense now.

  55. anonymous
    • one year ago
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    Thank you again for the help.

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