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

When cooking frozen ravioli, more water is used to maintain a stable temperature after adding the cold ravioli. Calculations using the specific heat capacity of the ravioli and water show how the temperature drops differently with 3 quarts vs 1 quart. More water ensures a consistent cooking temperature for even cooking.

Step-by-step explanation:

When cooking frozen cheese ravioli, using more water than necessary helps maintain a stable temperature in the pot during the cooking process. The specific heat capacity of the ravioli is 0.4 cal/g°C, which allows us to calculate the change in temperature of the water when the ravioli is added.

a. Temperature drop with 3 quarts of water:

We'll start by converting the water's mass to grams (1 quart of water is approximately 946.35 grams).

Mass of water = 3 quarts × 946.35 g/quart = 2839.05 g

We'll assume that the water was initially at boiling point, which is 100°C, and that the ravioli were at -40°C.

The heat lost or gained is given by the equation Q = mcΔT, where
m = mass of substance (in grams),
c = specific heat capacity,
ΔT = change in temperature.

To conserve energy, the heat gained by the ravioli will equal the heat lost by the water:

Q (ravioli) = Q (water)

(255 g)(0.4 cal/g°C)(T - (-40°C)) = (2839.05 g)(1 cal/g°C)(100°C - T)

After solving for T, we can find the new equilibrium temperature and thus the drop in temperature of the water.

b. Temperature drop with 1 quart of water:

If we only used 1 quart of water:

(255 g)(0.4 cal/g°C)(T - (-40°C)) = (946.35 g)(1 cal/g°C)(100°C - T)

Again, solving for T will give us the temperature drop when using less water.

The reason for using 3 quarts is that more water has a larger thermal mass, thus it is better at maintaining a steady temperature when cold food is added, providing a more consistent cooking environment and helping the ravioli to cook evenly.

Answer 2

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.

Step-by-step explanation:

Given:

• mass of frozen cheese,
  `m_c=255\ g`

• quantity of water suggested for the given cheese,
  `m_w=3\ quarts* 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* c_c* \Delta T=m_w* c_w* \Delta T`

`255* 0.4* (T_f-(-40))=2839.05* 1* (100-T_f)`

`T_f=95.14^(\circ)C`

b.

when using 1 quart of water:

`255* 0.4* (T_f-(-40))=946.35* 1* (100-T_f)`

`T_f=86.4^(\circ)C`

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