Suppose a chunk of metal is immersed in boiling water (10degreesC), then is quickly transferred into a Styrofoam cup containing 250g of water at 20Celcius. After a minute or so, the temp of contents are 24Celcius. Assume no significant energy is transferred between the contents of the cup & surroundings. The heat cap. of cup is negligible.
All I'm wondering for these are the equations I should use. I've written out how I would go about solving the problem, if you could tell me if I have the right idea that would be great.
a) How much heat is gained by the water?
b) How much is lost by the metal?
So for these two, I thought originally I would use the heat conduction equation? So, Q/t = kA (Th-Tc / L). Except now after typing it, I realize I don't have L. So now for a) I'm thinking Q = cmDeltaT..Would I sub in the water heat capacity for c, mass for m, and then the delta T as -4Celcius? And then Q would give me how much heat was gained by the water? Or lost by the metal?
For b), I'm thinking the same equation, but instead Q = CDeltaT, the Q would be the Q i got from a), the C would be the unknown, and Delta T would be the -4Celcius??
I'm really confused about this question Thank you for your help in advance
To solve this problem, we need to consider the heat gained by the water and the heat lost by the metal separately. You're on the right track with the equations, but let me clarify the steps for you.
a) To find the amount of heat gained by the water, we can use the equation:
Q = m * c * ΔT
where Q is the heat gained, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.
In this case, you have the mass of water (250g) and the change in temperature (ΔT = 24°C - 20°C = 4°C). The specific heat capacity of water is approximately 4.18 J/g°C. Plugging in these values, the equation becomes:
Q = 250g * 4.18 J/g°C * 4°C
By calculating this, you will find the amount of heat gained by the water.
b) To find the amount of heat lost by the metal, we can use a similar equation:
Q = m * C * ΔT
where Q is the heat lost, m is the mass of the metal, C is the specific heat capacity of the metal, and ΔT is the change in temperature.
In this case, we don't know the specific heat capacity of the metal (C), but we can find it using the heat lost by the metal (which can be assumed to be equal to the heat gained by the water). So we can rearrange the equation as:
C = Q / (m * ΔT)
You can substitute the heat lost (Q) from part a) and the mass and change in temperature of the metal into this equation to find the specific heat capacity of the metal.
Note that the negative sign in the change in temperature (ΔT = -4°C) indicates a decrease in temperature.
By following these steps, you should be able to find the answers to parts a) and b) using the appropriate equations.