46.9 g of a substance at 90.8°C is added to 51.8 g of water at 24.8°C. The final temperature of the water and substance is 40.5°C. The specific heat of water is 4.184 J/g·°C. What is the specific heat of the substance?
I think the equation that I need to use for this is C=Q/m * delta T. But I'm not sure
I think you are right but I like this way of doing it better.
loss of heat from substance + heat gained by water = 0
[mass substance x specific heat substance x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial) = 0 Solve for specific heat substance.
You are on the right track! The equation you mentioned, C = Q/m * ΔT, is correct. This equation relates the specific heat (C) of a substance to the amount of heat transferred (Q), the mass (m) of the substance, and the change in temperature (ΔT).
In this problem, we are given the masses and temperatures of both the substance and the water, as well as the final temperature. We want to find the specific heat of the substance.
To solve this, we can follow these steps:
1. Calculate the heat absorbed by the water:
Q_water = m_water * C_water * ΔT_water
where:
m_water is the mass of water
C_water is the specific heat of water
ΔT_water is the change in temperature of water
2. Calculate the heat absorbed by the substance:
Q_substance = m_substance * C_substance * ΔT_substance
where:
m_substance is the mass of the substance
C_substance is the specific heat of the substance
ΔT_substance is the change in temperature of the substance
3. Since the heat lost by the substance is equal to the heat gained by the water (according to the law of conservation of energy), we can set the two equations equal to each other:
Q_water = Q_substance
4. Rearrange the equation to solve for the specific heat of the substance (C_substance):
C_substance = Q_water / (m_substance * ΔT_substance)
Plugging in the given values, the equation becomes:
C_substance = (m_water * C_water * ΔT_water) / (m_substance * ΔT_substance)
Now, substitute the values into the equation and calculate the answer.