A 410-g cylinder of brass is heated to 95.0°C and placed in a calorimeter containing 335 g of water at 25.0°C. The water is stirred, and its highest temperature is recorded as 32.0°C. From the thermal energy gained by the water, determine the specific heat of brass. The specific heat of water is 4.18J/g*C. Show your work.
let b = specific heat of brass
410 * s * (95.0 - 32.0) = 335 * 4.18 * (32.0 - 25.0)
Thank you!
To solve this problem, we need the equation for heat transfer:
Q = mcΔT
Where:
Q = Heat transferred (in joules)
m = mass (in grams)
c = specific heat (in J/g°C)
ΔT = Change in temperature (in °C)
We can determine the heat transferred to the water by using the equation:
Q_water = m_water * c_water * ΔT_water
Given data:
m_water = 335 g (mass of water)
c_water = 4.18 J/g°C (specific heat of water)
ΔT_water = 32.0°C - 25.0°C = 7.0°C (change in temperature of water)
Substituting the values into the equation:
Q_water = 335 g * 4.18 J/g°C * 7.0°C
= 9831.85 J
Since the heat transferred from the brass to the water is equal to the heat gained by the water, we can set up an equation to solve for the specific heat of brass:
Q_brass = m_brass * c_brass * ΔT_water
Given data:
m_brass = 410 g (mass of brass)
ΔT_water = 7.0°C (change in temperature of water)
Substituting the values into the equation:
9831.85 J = 410 g * c_brass * 7.0°C
To solve for c_brass, divide both sides of the equation by (410 g * 7.0°C):
c_brass = 9831.85 J / (410 g * 7.0°C)
≈ 3.00 J/g°C
Therefore, the specific heat of brass is approximately 3.00 J/g°C.
To determine the specific heat of brass, we need to calculate the thermal energy gained by the water. We can use the equation:
Q = m * c * ΔT
Where:
Q = thermal energy gained/lost by the water (in Joules)
m = mass of water (in grams)
c = specific heat capacity of water (in J/g°C)
ΔT = change in temperature of water (final temperature - initial temperature, in °C)
In this case, the mass of water (m) is given as 335 g, the specific heat capacity of water (c) is 4.18 J/g°C, and the change in temperature of the water (ΔT) is 32°C - 25°C = 7°C.
Substituting these values into the equation:
Q = 335 g * 4.18 J/g°C * 7°C
Q = 9925.9 J (rounding off to four significant figures)
The thermal energy gained by the water is 9925.9 J.
Now, we can use the fact that the thermal energy gained by the water is equal to the thermal energy lost by the brass. We can use the same equation as above to calculate the thermal energy lost by the brass, but this time we need to determine the specific heat capacity of brass (C).
Q = m * C * ΔT
Where:
Q = thermal energy gained/lost by the brass (in Joules)
m = mass of brass (in grams)
C = specific heat capacity of brass (in J/g°C)
ΔT = change in temperature of brass (final temperature - initial temperature, in °C)
In this case, the mass of brass (m) is given as 410 g, the change in temperature of the brass (ΔT) is 95°C - 25°C = 70°C, and the thermal energy gained by the brass (Q) is 9925.9 J.
Substituting these values into the equation:
9925.9 J = 410 g * C * 70°C
Solving for C:
C = 9925.9 J / (410 g * 70°C)
Finally, calculating C:
C = 0.346 J/g°C (rounding off to three significant figures)
The specific heat capacity of brass is approximately 0.346 J/g°C.