If a piece of granite weighing 250.0 grams is heated in boiling water to a temperature of 100 C and then placed in a calorimeter containing 400.00 grams of water, the temperature of the water increases from 20.0 C to 28.5 C. what is the specific heat of Granite?
The sum of the heats gained is zero (one loses heat).
heatgainedgrannite+heatgainedwater=0
250*Cgran*( 28.5-100)+400*cwater*(28.5-20)=0
solve for specific heat of granite.
heat lost by granite + heat gained by H2O = 0
[mass granite x specific heat granit x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve for specific heat granite, the only unknown.
To determine the specific heat of granite, we can use the principle of energy conservation. The energy gained by the water is equal to the energy lost by the granite.
Let's break down the steps:
Step 1: Calculate the energy gained by the water.
The formula to calculate the energy gained is given by: Q_water = m_water * c_water * ΔT_water
Where:
Q_water is the energy gained by the water,
m_water is the mass of water,
c_water is the specific heat capacity of water,
ΔT_water is the change in temperature of the water.
Given:
m_water = 400.00 grams,
c_water = 4.18 J/g°C,
ΔT_water = 28.5°C - 20.0°C = 8.5°C
Plugging in the values, we get:
Q_water = 400.00 g * 4.18 J/g°C * 8.5°C = 14234.00 J
Step 2: Calculate the energy lost by the granite.
The formula to calculate the energy lost by the granite is given by: Q_granite = m_granite * c_granite * ΔT_granite
Where:
Q_granite is the energy lost by the granite,
m_granite is the mass of granite,
c_granite is the specific heat capacity of granite,
ΔT_granite is the change in temperature of the granite.
Given:
m_granite = 250.0 grams,
ΔT_granite = 100°C - 20.0°C = 80.0°C (heated in boiling water)
Since we need to calculate the specific heat of granite, we rearrange the equation:
c_granite = Q_granite / (m_granite * ΔT_granite)
Plugging in the known values, we get:
c_granite = 14234.00 J / (250.0 g * 80.0°C) = 0.713 J/g°C
Therefore, the specific heat of granite is approximately 0.713 J/g°C.
To find the specific heat of granite, we need to use the equation:
Q = mcΔT,
where Q is the heat energy absorbed or released, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, the heat energy absorbed by the water can be calculated using:
Q_water = m_water * c_water * ΔT_water
where m_water is the mass of water, c_water is the specific heat capacity of water, and ΔT_water is the change in temperature of water.
The heat energy released by the granite can be calculated using:
Q_granite = m_granite * c_granite * ΔT_granite
where m_granite is the mass of the granite, c_granite is the unknown specific heat capacity of granite, and ΔT_granite is the change in temperature of the granite.
Since the heat energy released by the granite is absorbed by the water, we can equate Q_water and Q_granite:
Q_water = Q_granite
Now we can substitute the known values into the equation and solve for the specific heat capacity of granite:
m_water * c_water * ΔT_water = m_granite * c_granite * ΔT_granite
m_water = 400.00 grams (mass of water)
c_water = 4.18 J/g·°C (specific heat capacity of water)
ΔT_water = 28.5°C - 20.0°C (change in temperature of water)
m_granite = 250.0 grams (mass of granite)
ΔT_granite = 100°C - 20.0°C (change in temperature of granite)
Now we can plug in the values:
400.00 grams * 4.18 J/g·°C * (28.5°C - 20.0°C) = 250.0 grams * c_granite * (100°C - 20.0°C)
Solving for c_granite:
c_granite = [400.00 grams * 4.18 J/g·°C * (28.5°C - 20.0°C)] / [250.0 grams * (100°C - 20.0°C)]
c_granite = 1.29 J/g·°C
Therefore, the specific heat capacity of granite is approximately 1.29 J/g·°C.