Question

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?

Answer 1

Answer:

a. $T_f=95.14^{\circ}C$

b. $T_f=86.4^{\circ}C$

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

Explanation:

Given:

• mass of frozen cheese, $m_c=255\ g$

• quantity of water suggested for the given cheese, $m_w=3\ quarts\times 946.35=2839.05\ g$

• initial temperature of cheese, $T_{ic}=-40^{\circ}\ C$

• specific heat of cheese, $c_c=0.4\ cal.g^{-1}.^{\circ}C^{-1}$

• initial temperature of water, $T_{iw}=100^{\circ}\ C$

a.

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

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

$m_c\times c_c\times \Delta T=m_w\times c_w\times \Delta T$

$255\times 0.4\times (T_f-(-40))=2839.05\times 1\times (100-T_f)$

$T_f=95.14^{\circ}C$

b.

when using 1 quart of water:

$255\times 0.4\times (T_f-(-40))=946.35\times 1\times (100-T_f)$

$T_f=86.4^{\circ}C$

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