If 25.4 kg of copper at 33°C receives 240 kJ of heat. Calculate the final temperature of the metal.
Well, copper is known for conducting heat really well, so it's like the metal equivalent of an Olympic sprinter running away with that 240 kJ of heat. But, let's not get too carried away. To find the final temperature, we need to use the specific heat capacity of copper, which is approximately 0.385 J/g°C.
First, let's convert the given mass of copper into grams. 25.4 kg is equivalent to 25,400 g.
Next, we'll plug the values into the heat equation:
Q = mcΔT
Where:
Q = heat energy (240,000 J)
m = mass of copper (25,400 g)
c = specific heat capacity of copper (0.385 J/g°C)
ΔT = change in temperature (final temperature - initial temperature)
Now, let's solve for ΔT:
240,000 J = (25,400 g)(0.385 J/g°C)(ΔT)
Divide both sides of the equation by (25,400 g)(0.385 J/g°C) to isolate ΔT:
ΔT = 240,000 J / (25,400 g)(0.385 J/g°C)
Calculating the right side of the equation, we get:
ΔT ≈ 2.977°C
So, to find the final temperature, we add the change in temperature to the initial temperature:
Final temperature ≈ 33°C + 2.977°C ≈ 35.977°C
Therefore, the final temperature of the copper would be approximately 35.977°C. But hey, don't expect the copper to throw a thank-you party for receiving all that heat!
To solve this problem, we can use the equation:
Q = mcΔT
Where:
Q = Heat energy (in joules)
m = Mass of the substance (in kg)
c = Specific heat capacity of the substance (in J/kg⋅°C)
ΔT = Change in temperature (in °C)
First, let's find the specific heat capacity of copper. The specific heat capacity of copper is approximately 385 J/kg⋅°C.
Now we can rearrange the formula to solve for the change in temperature:
ΔT = Q / (mc)
Given:
m = 25.4 kg
c = 385 J/kg⋅°C
Q = 240 kJ = 240,000 J
Substituting the values:
ΔT = 240,000 J / (25.4 kg × 385 J/kg⋅°C)
ΔT ≈ 24.7 °C
To find the final temperature, we add the change in temperature to the initial temperature:
Final temperature = Initial temperature + ΔT
Given:
Initial temperature = 33 °C
Final temperature ≈ 33 °C + 24.7 °C
Final temperature ≈ 57.7 °C
Therefore, the final temperature of the copper is approximately 57.7 °C.
To solve this problem, we will use the equation:
Q = mcΔT
Where:
Q = Heat energy transferred to the object (in joules)
m = Mass of the object (in kilograms)
c = Specific heat capacity of the material (in joules per kilogram per degree Celsius)
ΔT = Change in temperature (in degrees Celsius)
First, let's calculate the Heat energy transferred to the copper using the given information:
Q = 240 kJ = 240,000 J (since 1 kJ = 1000 J)
Next, we need to find the specific heat capacity of copper. The specific heat capacity of copper is approximately 385 J/(kg·°C).
Now, we can substitute the values into the equation and solve for ΔT:
240,000 = (25.4 kg) × (385 J/(kg·°C)) × ΔT
Simplifying the equation:
ΔT = 240,000 J / (25.4 kg × 385 J/(kg·°C))
Calculating the value:
ΔT ≈ 24.82 °C
To find the final temperature, we need to add the change in temperature (ΔT) to the initial temperature. The initial temperature is given as 33°C:
Final temperature = 33°C + 24.82°C
Final temperature ≈ 57.82°C
Therefore, the final temperature of the copper is approximately 57.82°C.
q = mass Cu x specific heat Cu x (Tfinal-Tinitial)
Watch the units. I would use J for q, g for mass and specific unit (you will need to look that up in your text or notes) in units of J/g*C