The lowest temperature ever recorded in Alaska is-6 C. The highest temperature ever recorded in Alaska is 38°C. Suppose a piece of metal with a mass of 180 g and a temperature of -62.0°C is placed in a calorimeter containing 0.500 kg of water with a temperature of 38.0°C. If the final equilibrium temperature of the metal and water is 36.9°C, what is the specific heat capacity of the metal? Use the calculated value of the specific heat capacity to identify the metal.
I forgot to include that the answer is 130 J/kg x Celsius
metal mass = 0.180 kg
0.180 (36.9 - - 62) C = 0.500 (38-36.9)(about 4000 Joules/ kg deg C)
.18* 98.9 C = 1.1 * 2000
C =124 J/kg degC
To find the specific heat capacity of the metal, you can use the principle of conservation of energy, which states that the heat lost by the metal is equal to the heat gained by the water.
The heat lost by the metal can be calculated using the equation:
Q = mcΔT
Where:
Q is the heat lost by the metal (in Joules)
m is the mass of the metal (in kg)
c is the specific heat capacity of the metal (in J/(kg·°C))
ΔT is the change in temperature of the metal (in °C)
The heat gained by the water can be calculated using the equation:
Q = mcΔT
Where:
Q is the heat gained by the water (in Joules)
m is the mass of the water (in kg)
c is the specific heat capacity of water (4,184 J/(kg·°C)) since it is water
ΔT is the change in temperature of the water (in °C)
Since the final equilibrium temperature is 36.9°C, the change in temperature for the metal and the water can be calculated as:
ΔT_metal = final temperature - initial temperature = 36.9°C - (-62.0°C) = 98.9°C
ΔT_water = final temperature - initial temperature = 36.9°C - 38.0°C = -1.1°C
Now we can substitute the given values into the equations to solve for the specific heat capacity of the metal:
Q_metal = mcΔT_metal
Q_water = mcΔT_water
Since the heat lost by the metal is equal to the heat gained by the water:
Q_metal = Q_water
mcΔT_metal = mcΔT_water
(metal specific heat capacity) × (mass of the metal) × (change in temperature of the metal) = (specific heat capacity of water) × (mass of the water) × (change in temperature of the water)
c_metal × (0.180 kg) × (98.9°C) = (4,184 J/(kg·°C)) × (0.500 kg) × (-1.1°C)
Now we can solve for the specific heat capacity of the metal:
c_metal = [(4,184 J/(kg·°C)) × (0.500 kg) × (-1.1°C)] / [(0.180 kg) × (98.9°C)]
c_metal = -0.134 J/(g·°C)
The negative sign indicates that heat is being transferred from the metal to the water. Since the specific heat capacity of the metal is negative, it suggests an exothermic reaction.
As for identifying the metal, more information is needed. The specific heat capacity value alone is not sufficient to identify the metal accurately. It would be helpful to know the specific heat capacity values of different metals and compare them with the calculated value to identify the metal.
To find the specific heat capacity of the metal, we can use the principle of heat transfer, which states that the heat lost by the hot object is equal to the heat gained by the cold object when they reach thermal equilibrium.
First, let's calculate the heat gained by the water:
q_water = m_water * c_water * ΔT_water
Where:
q_water represents the heat gained by the water,
m_water is the mass of the water (0.500 kg),
c_water is the specific heat capacity of water (4.18 J/g°C), and
ΔT_water is the change in temperature of the water (final temperature - initial temperature).
ΔT_water = 36.9°C - 38.0°C = -1.1°C
Now we can calculate q_water:
q_water = (0.500 kg) * (4.18 J/g°C) * (-1.1°C)
Since the specific heat capacity for water is given in joules per gram per degree Celsius, we need to convert the mass of water from kilograms to grams:
q_water = (0.500 kg * 1000 g/kg) * (4.18 J/g°C) * (-1.1°C)
q_water = -2309 J
According to the principle of heat transfer, the heat lost by the water is equal to the heat gained by the metal:
q_water = q_metal
Now we can calculate the heat gained by the metal:
q_metal = m_metal * c_metal * ΔT_metal
Where:
q_metal represents the heat gained by the metal,
m_metal is the mass of the metal (180 g),
c_metal is the specific heat capacity of the metal, and
ΔT_metal is the change in temperature of the metal (final temperature - initial temperature).
ΔT_metal = 36.9°C - (-62.0°C) = 98.9°C
Now we can solve for c_metal:
c_metal = q_metal / (m_metal * ΔT_metal)
Substituting the known values:
c_metal = -2309 J / (180 g * 98.9°C)
c_metal = -2309 J / 17,802 g°C
c_metal ≈ -0.13 J/g°C
Since the specific heat capacity of the metal cannot be negative, there seems to be an error in the calculations. Please check the entered values and calculations again to ensure accuracy.