What is the effect on water temperature when pasta is added to boiling water?

[pentazoid]

Homework Statement

The specific heat capacity of Albertsons pasta is approximately 1.8 J/g*C degrees. Suppose you toss 340 g of this pasta (at 25 degrees celsuis) into 1.5 liters of boiling water. What effect does this have on the temperature of water. (before there is time for stove to add more heat)?

Homework Equations

Q=c*m*delta(T)

The Attempt at a Solution

When the 25 degree pasta is tossed into boiling stove of water, doesn't the temperature of the stove decrease and the temperature of pasta increase? What physical quantity do I need to mathematically determined to find out the effect ?

 

[LowlyPion]

You have 1.5 liters of water at 100°.

Now you've added 340g of something that is 25°.

You can calculate the amount of heat capacity that the pasta will absorb and that if taken from the water, the temp that it will bring the water down to, taking into account the water to steam latent heat?

 

[pentazoid]

You have 1.5 liters of water at 100°.

Now you've added 340g of something that is 25°.

You can calculate the amount of heat capacity that the pasta will absorb and that if taken from the water, the temp that it will bring the water down to, taking into account the water to steam latent heat?

Q_initial = Q_final?

Q_initial=c*m*delta(T)?

m_water=rho_water*V_water?

c_noodles*m_noodles*delta(T)=m_water*c_water*delta(T)

HOw would I determine the delta(T) for the noodles and delta(T) for the water?

 

[gjfleischman]

(before there is time for stove to add more heat)?

This is the crux of the matter--time. The temperature obtained by equating the heat gained by the pasta with the heat lost by the water is only for a final equilibrium state (i.e., heat is no longer exchanged) in an adiabatic system, which you do not have if the water is being heated by the stove. Instead, what you have is a standard transient heat transfer problem in which thermal conductivity plays a role in addition to heat capacity, density and mass. An additional parameter, the surface heat transfer coefficient, is also necessary.

But the problem is not well defined. The question is about the temperature of the water. But because it is time-dependent, the question cannot be answered until a time is stipulated. A long enough time, as noted, would allow the water to "recover" and come back to close to its initial temperature because it's being heated by the stove. Any time sooner than that would require transient heat transfer analysis. In this case you would be dealing with a partial differential equation. Water would be your system and your boundary conditions would your heat input from the stove, and heat lost to the pasta, heat lost to the environment by conduction and heat lost via steam creation. Heat lost to the pasta requires knowing the surface heat transfer coefficient of the pasta which would have to be obtained experimentally.

Even with all this, the problem is still unwieldy and requires assumptions to simplify it. But you wouldn't know the relevance of some of those assumptions unless you did actual experiments. For example, one assumption is that boiling keeps the water well mixed so that although temperature changes, it stays uniform throughout the pot. Another assumption is that if the time is short enough, heat lost via steam may be neglected.

One big simplification is assuming that heat loss to the pasta occurs such that water temperature stays steady. First, before the introduction of the pasta, the water is at a steady state--there's enough heat coming from the stove to balance the heat lost via steam production of a steady boil. Then the pasta is added and while it is being heated, the water assumes a new, lower, temperature that is steady. Instead of the heat input of the stove balancing heat loss to steam production, it now balances heat loss to the pasta. I don't know if this assumption is justifiable.

Adding thorough mixing to the simplification just discussed removes the thermal conductivity from the problem, but not the surface heat transfer coefficient. So, regardless of simplifications, this is not simply a heat capacity problem.