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When cooking frozen cheese ravioli, the directions say to put the 255 grams of filled pasta into 3 quarts of boiling water. Why should you use 3 quarts when 1 quart would easily cover them all? Suppose they are in the freezer at - 40 °C. You may consider the ravioli to have a specific heat of 0.4 cal/gam-°C both when frozen and when in water.

a. By how much does the temperature of the 3 quarts of water drop when you add the frozen ravioli?
b. How much would the water temperature drop if you used only 1 quart? Why do they ask for 3 quarts?

Respuesta :

Answer:

a. [tex]T_f=95.14^{\circ}C[/tex]

b. [tex]T_f=86.4^{\circ}C[/tex]

It is asked for 3 quarts of water  because it prevents the temperature drop.

Explanation:

Given:

  • mass of frozen cheese, [tex]m_c=255\ g[/tex]
  • quantity of water suggested for the given cheese, [tex]m_w=3\ quarts\times 946.35=2839.05\ g[/tex]
  • initial temperature of cheese, [tex]T_{ic}=-40^{\circ}\ C[/tex]
  • specific heat of cheese, [tex]c_c=0.4\ cal.g^{-1}.^{\circ}C^{-1}[/tex]
  • initial temperature of water, [tex]T_{iw}=100^{\circ}\ C[/tex]

a.

  • we have specific heat of water, [tex]c_w=1\ cal.g^{-1}.^{\circ}C^{-1}[/tex]

so now, we use the heat equation to find the amount of heat exchange during the process:

[tex]m_c\times c_c\times \Delta T=m_w\times c_w\times \Delta T[/tex]

[tex]255\times 0.4\times (T_f-(-40))=2839.05\times 1\times (100-T_f)[/tex]

[tex]T_f=95.14^{\circ}C[/tex]

b.

when using 1 quart of water:

[tex]255\times 0.4\times (T_f-(-40))=946.35\times 1\times (100-T_f)[/tex]

[tex]T_f=86.4^{\circ}C[/tex]

It is asked for 3 quarts of water  because it prevents the temperature drop.

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