A 395-g cylinder is heated to 75°C and placed in a calorimeter containing 405 g of water at 25°C.
The water is stirred, and its highest temperature is recorded as 38°C. From the thermal energy
gained by the water, determine the specific heat of the material the cylinder is constructed of.
The specific heat of water is 4.18 J/g·°C.
To determine the specific heat of the material the cylinder is constructed of, we need to use the formula:
Q = m × c × ΔT
Where:
Q is the thermal energy gained by the water
m is the mass of the water
c is the specific heat of the material
ΔT is the change in temperature of the water
First, let's calculate the thermal energy gained by the water:
Q = m × c × ΔT
Q = 405 g × 4.18 J/g·°C × (38°C - 25°C)
Q = 405 g × 4.18 J/g·°C × 13°C
Q = 21,430.35 J
Now, let's calculate the specific heat of the material:
Q = m × c × ΔT
21,430.35 J = 395 g × c × (38°C - 75°C)
21,430.35 J = 395 g × c × -37°C
Divide both sides by -37°C:
-21,430.35 J / -37°C = 395 g × c
579.49 J/°C = 395 g × c
Finally, divide both sides by 395 g:
579.49 J/°C / 395 g = c
c ≈ 1.47 J/g·°C
Therefore, the specific heat of the material the cylinder is constructed of is approximately 1.47 J/g·°C.
To find the specific heat of the material the cylinder is constructed of, we need to use the formula:
Heat gained by water = (mass of water) x (specific heat of water) x (change in temperature of water)
First, let's calculate the heat gained by the water.
The mass of water is given as 405 g.
The specific heat of water is given as 4.18 J/g·°C.
The change in temperature of water is (38°C - 25°C) = 13°C.
So, the heat gained by the water is:
Heat gained by water = (405 g) x (4.18 J/g·°C) x (13°C)
Now, let's calculate the heat gained by the water using the mass and specific heat of the cylinder's material.
The mass of the cylinder is given as 395 g.
Let's assume the specific heat of the cylinder's material as 'x' J/g·°C.
The change in temperature of the cylinder's material is (38°C - 75°C) = -37°C (since it was heated, the change in temperature is negative).
The heat gained by the cylinder's material is:
Heat gained by cylinder = (395 g) x (x J/g·°C) x (-37°C)
According to the principle of conservation of energy, the heat gained by the cylinder's material should equal the heat gained by the water.
So, we have the equation:
(405 g) x (4.18 J/g·°C) x (13°C) = (395 g) x (x J/g·°C) x (-37°C)
Let's solve the equation to find the specific heat of the cylinder's material 'x':
(405 g) x (4.18 J/g·°C) x (13°C) = (395 g) x (x J/g·°C) x (-37°C)
Simplifying the equation:
(405) x (4.18) x (13) = (395) x (-37) x (x)
Now, let's solve for 'x':
(405) x (4.18) x (13) = (395) x (-37) x (x)
Solving for 'x':
(x) = [(405) x (4.18) x (13)] / [(395) x (-37)]
Use your calculator to evaluate the right-hand side of the equation.
Therefore, by finding the value of 'x', you can determine the specific heat of the material the cylinder is constructed of.