Two bars of identical mass are at 29 °C. One is made from glass and the other from another substance. The specific heat capacity of glass is 840 J/(kg · C°). When identical amounts of heat are supplied to each, the glass bar reaches a temperature of 92 °C, while the other bar reaches 285.0 °C. What is the specific heat capacity of the other substance?
To find the specific heat capacity of the other substance, we can use the formula:
Q = mcΔT
Where:
Q is the amount of heat transferred
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
First, let's analyze the situation:
1. The two bars have identical mass and are initially at the same temperature.
2. Identical amounts of heat are supplied to both bars.
3. The glass bar reaches a temperature of 92 °C.
4. The other bar reaches a temperature of 285.0 °C.
Since the mass and heat supplied are the same for both bars, we can assume that Q and ΔT are equal for both bars. Let's represent them as Q1 and ΔT1 for the glass bar and Q2 and ΔT2 for the other bar.
For the glass bar:
Q1 = mcΔT1
For the other substance:
Q2 = mcΔT2
Since Q and ΔT are equal for both bars, we have:
mcΔT1 = mcΔT2
Canceling the mass from both equations, we get:
cΔT1 = cΔT2
Now we can solve for the specific heat capacity of the other substance (c2):
c2 = (cΔT2) / ΔT1
Substituting the given values:
c2 = (840 J/(kg · C°) * (285.0 °C - 29 °C)) / (92 °C - 29 °C)
Simplifying the equation:
c2 = (840 J/(kg · C°) * 256 °C) / 63 °C
c2 = 3427.5 J/(kg · C°)
Therefore, the specific heat capacity of the other substance is 3427.5 J/(kg · C°).