Substances A and B with the same mass and the same initial temperature absorb the same amount of heat energy. The final temperature of A is higher than the final temperature of B. Which substance would have the higher specific heat? Why?
We know q = mass x specific heat x delta T; therefore, let's solve for specific heat (which we can conveniently call X).
XA = qA/(massA x delta T)
XB</sbu> = qB/(massB x delta T).
If qA = qB and massA = massB, then the only difference is delta T. Which is the larger delta T. A larger delta T (in the denominator) means a what (smaller?) X.
To determine which substance would have the higher specific heat, we need to understand the concept of specific heat and how it relates to the change in temperature.
Specific heat (C) is a property of a substance and represents the amount of heat energy required to raise the temperature of one unit mass of that substance by one degree Celsius (or Kelvin). Mathematically, it is expressed as:
C = Q / (m * ΔT),
where C is the specific heat, Q is the heat energy absorbed or released, m is the mass of the substance, and ΔT is the change in temperature.
In the given scenario, substances A and B have the same mass and absorb the same amount of heat energy. However, the final temperature of A is higher than the final temperature of B. This means that substance A experiences a greater change in temperature (ΔT) compared to substance B, given the same amount of heat energy.
Given that Q and m are the same for both substances, the change in temperature (ΔT) is the only variable that can affect the specific heat.
Using the specific heat formula mentioned earlier, we can rearrange it to solve for Q:
Q = C * (m * ΔT).
Since the same Q is absorbed by both substances, and m is the same, we can see that for substance A to have a higher final temperature and the same Q, it must have a smaller change in temperature (ΔT) compared to substance B.
Since ΔT is smaller for substance A, we can conclude that substance A must have a higher specific heat (C) than substance B. This is because a higher specific heat means that it requires more heat energy to produce the same change in temperature, which is exactly what we observed with substance A in the given scenario.
Therefore, based on the information provided, substance A would have the higher specific heat, as it requires more heat energy to raise its temperature compared to substance B.