when 200 grams of aluminum at 100 degrees celsius is dropped into an aluminum calorimeter of mass 120 grams and containing 150 grams of kerosene at 15 degrees celsius,the mixtures reaches a temperature of 50 degrees celsius.what is the specific heat of kerosene?
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To find the specific heat of kerosene, we can use the principle of energy conservation.
First, let's calculate the heat gained by the aluminum and the calorimeter. We will use the formula:
Q = mcΔT
where Q is the heat gained or lost, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Heat gained by the aluminum:
Q_aluminum = m_aluminum * c_aluminum * ΔT_aluminum
Q_aluminum = 200 g * c_al (specific heat of aluminum) * (50°C - 100°C)
Heat gained by the calorimeter:
Q_calorimeter = m_calorimeter * c_calorimeter * ΔT_calorimeter
Q_calorimeter = 120 g * c_al (specific heat of aluminum) * (50°C - 15°C)
Since the heat gained by the aluminum is transferred to the calorimeter, we can equate the two equations:
Q_aluminum = Q_calorimeter
200 g * c_al * (50°C - 100°C) = 120 g * c_al * (50°C - 15°C)
Simplifying the equation:
-15000 g c_al = -6000 g c_al
Dividing both sides by -15000 g and canceling out the c_al term:
c_al = -6000 g / -15000 g
c_al = 0.4 cal/g°C
Since the heat gained by the aluminum is transferred to the kerosene, we can equate the heat gained by the aluminum with the heat gained by the kerosene:
Q_aluminum = Q_kerosene
200 g * c_al * (50°C - 100°C) = 150 g * c_kerosene * (50°C - 15°C)
Substituting the value of c_al with 0.4 cal/g°C:
200 g * 0.4 cal/g°C * (50°C - 100°C) = 150 g * c_kerosene * (50°C - 15°C)
-2000 cal = 150 g c_kerosene * 35°C
Simplifying the equation:
-2000 cal = 5250 g c_kerosene
Dividing both sides by 5250 g and canceling out the c_kerosene term:
c_kerosene = -2000 cal / 5250 g
c_kerosene ≈ 0.38 cal/g°C
Therefore, the specific heat of kerosene is approximately 0.38 cal/g°C.
To find the specific heat of kerosene, you need to use the principle of conservation of energy. The heat lost by the aluminum is equal to the heat gained by the kerosene and the calorimeter.
Step 1: Calculate the heat lost by the aluminum:
Heat lost by aluminum = mass of aluminum × specific heat of aluminum × change in temperature
= 200 g × specific heat of aluminum × (50 - 100) degrees Celsius
Step 2: Calculate the heat gained by the calorimeter and kerosene:
Heat gained by calorimeter and kerosene = (mass of calorimeter + mass of kerosene) × specific heat of kerosene × change in temperature
= (120 g + 150 g) × specific heat of kerosene × (50 - 15) degrees Celsius
Step 3: Equate the heat lost by the aluminum to the heat gained by the calorimeter and kerosene:
200 g × specific heat of aluminum × (50 - 100) degrees Celsius = (120 g + 150 g) × specific heat of kerosene × (50 - 15) degrees Celsius
Step 4: Solve for the specific heat of kerosene:
specific heat of kerosene = (200 g × specific heat of aluminum × (50 - 100) degrees Celsius) / ((120 g + 150 g) × (50 - 15) degrees Celsius)
Now, substitute the known values into the formula and calculate the specific heat of kerosene. The specific heat of aluminum is typically around 0.897 J/g°C.