What will be the final temperature if 2000g of copper at 95 degrees loses 10 kcal of heat?
What will be the final temperature if 2000g of copper at 95 degrees loses 10 kcal of heat?
Well, if 2000g of copper loses 10 kcal of heat, it's going to be a really cooling experience for the copper! But don't worry, I'll give you a serious answer anyway. To solve this, we can use the specific heat capacity of copper, which is approximately 0.39 J/g°C.
Since we have 2000g of copper and it loses 10 kcal (which is equivalent to 41,840 J) of heat, we can calculate the change in temperature using the formula Q = m * c * ΔT. Rearranging the formula, we have ΔT = Q / (m * c).
Substituting the values, we get ΔT = 41,840 J / (2000g * 0.39 J/g°C). Doing the math, we find that ΔT is approximately 54.05°C.
So, the final temperature of the copper would be 95°C - 54.05°C = 40.95°C.
Voilà! The copper will transform from a hot head to a cool customer, ending up at approximately 40.95°C.
To find the final temperature of the copper, we can use the heat equation:
Q = mcΔT
Where:
Q is the heat transferred (in calories or kcal)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in calories/gram °C or kcal/gram °C)
ΔT is the change in temperature (in °C)
First, let's determine the specific heat capacity of copper. The specific heat capacity of copper is approximately 0.39 kcal/g °C.
Next, we can substitute the known values into the heat equation:
Q = mcΔT
-10 kcal = (2000g)(0.39 kcal/g °C)ΔT
Simplifying the equation:
-10 kcal = 780 g°C ΔT
Now we can solve for ΔT:
ΔT = -10 kcal / (780 g°C)
ΔT ≈ -0.0128°C
So, the change in temperature is approximately -0.0128°C.
To find the final temperature, we can subtract the change in temperature from the initial temperature:
Final temperature = 95°C - 0.0128°C
Final temperature ≈ 94.9872°C
Therefore, the final temperature of the copper will be approximately 94.9872°C.
To determine the final temperature of a substance after losing a certain amount of heat, we can use the formula:
Q = m * c * ΔT
where:
Q is the amount of heat transferred,
m is the mass of the substance,
c is the specific heat capacity of the substance, and
ΔT is the change in temperature.
In this case, we have:
m = 2000g (mass of copper)
c = specific heat capacity of copper (approximately 0.39 J/g°C)
ΔT = final temperature - initial temperature
We also have the amount of heat transferred, which is given as 10 kcal. To convert kcal to Joules, we can use the conversion factor 1 kcal = 4.18 kJ = 4180 J.
So, let's calculate ΔT:
10 kcal * 4180 J/kcal = 41800 J
41800 J = 2000g * 0.39 J/g°C * ΔT
ΔT = 41800 J / (2000g * 0.39 J/g°C)
By solving this equation, we can find the change in temperature, ΔT. Then we can calculate the final temperature by subtracting the change in temperature from the initial temperature.
Let me calculate that for you:
ΔT = 41800 J / (2000g * 0.39 J/g°C) ≈ 53.85 °C
The initial temperature is 95 °C, so the final temperature will be:
Final temperature = 95 °C - 53.85 °C ≈ 41.15 °C
Therefore, the final temperature of the copper is approximately 41.15 °C.