A piece of metal of mass 50g heated to 100degree centigrade is dropped into 200g of water at 14degree centigrade In a copper calorimeter when 80g and raises the temperature to 70degree centigrade. Calculate the heat capacity of the piece of metal. Take specific heat capacity of copper=0.4joules grams per Kelvin while S H.C of water= 4.2joules grams per kelvin
1094j/kg/k
Give me answer
To calculate the heat capacity of the piece of metal (Cmetal), we can use the formula:
Q = m * c * ΔT
Where:
Q = Heat transferred (in joules)
m = Mass of the substance
c = Specific heat capacity of the substance
ΔT = Change in temperature
First, let's calculate the heat (Q) transferred from the metal to the water. We can use the formula:
Q = m * c * ΔT
Where:
m = Mass of the water
c = Specific heat capacity of water
ΔT = Change in temperature
The mass of water is given as 200g, the specific heat capacity of water is 4.2 joules/grams per Kelvin, and the change in temperature is (70 - 14)°C = 56°C.
Qwater = 200g * 4.2 J/g°C * 56°C = 47040 J
Next, let's calculate the heat transferred from the metal and absorbed by the water. We can use the formula:
Q = m * c * ΔT
Where:
m = Mass of the metal
c = Specific heat capacity of the metal
ΔT = Change in temperature
The mass of the metal is given as 80g, the specific heat capacity of copper is 0.4 joules/grams per Kelvin, and the change in temperature is (70 - 100)°C = -30°C.
Qmetal = 80g * 0.4 J/g°C * -30°C = -960 J
Since the metal loses heat to the water, the value of Qmetal is negative.
The total heat transferred from the metal to the water can be calculated by summing up Qwater and Qmetal:
Qtot = Qwater + Qmetal
= 47040 J + (-960 J)
= 46080 J
Now, we can calculate the heat capacity of the metal (Cmetal) by rearranging the formula:
Qtot = Cmetal * ΔTmetal
Rearranging the formula, we get:
Cmetal = Qtot / ΔTmetal
The change in temperature of the metal (ΔTmetal) is (100 - 70)°C = 30°C.
Cmetal = 46080 J / 30°C
= 1536 J/°C
Therefore, the heat capacity of the piece of metal is 1536 joules per degree Celsius (J/°C).
To calculate the heat capacity of the piece of metal, we need to use the principle of conservation of energy.
The heat gained by the metal is equal to the heat lost by the water and the copper calorimeter.
First, let's calculate the heat lost by water and the calorimeter.
The formula to calculate the heat lost or gained is:
Q = m * c * ΔT
Where:
Q = heat lost or gained
m = mass
c = specific heat capacity
ΔT = change in temperature
For the water and the calorimeter:
Q1 = (200g + 80g) * 4.2 J/g·K * (70°C - 14°C)
Q1 = 280g * 4.2 J/g·K * 56K
Q1 = 62,496 J
Next, let's calculate the heat gained by the metal. The mass of the metal is 50g, and the change in temperature is from 100°C to 70°C.
Q2 = 50g * c (specific heat capacity of the metal) * (70°C - 100°C)
To find the value of c, we can rearrange the formula:
Q2 = 50g * c * (-30°C)
Q2 = -1500g°C * c
Since we know that Q1 = Q2, we can equate the two equations and solve for c:
62,496 J = -1500g°C * c
c = 62,496 J / -1500g°C
c ≈ -41.664 J / g°C
The heat capacity of the piece of metal is approximately -41.664 J°C.