The question is: A 30g sample of metal with a specific heat of .34J/g is heated to 50C. 4.8KJ of energy was transferred. What is the initial temperature?
I used:
heat=(mass)(specific heat)(change in temp)
So I did 4800J=(30)(.34)(50-x)
4800=(10.2)(50-x)
4800=510-10.2x
4290=10.2
-420.59
This can't possibly be right. Can you tell me where I went wrong? Thanks!
You did the calculations correctly. I expect the writer of the problem did not think when she constructed the question.
Sure! Let's go through the problem and identify where you made a mistake.
First, let's write down the formula for heat:
Q = (m)(c)(ΔT)
Where:
Q = heat energy transferred (in joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in joules per gram per degree Celsius)
ΔT = change in temperature (in degrees Celsius)
In the given problem, you correctly identified the formula and plugged in the values:
Q = 4800 J
m = 30 g
c = 0.34 J/g°C
ΔT = 50°C - x (where x is the initial temperature)
Now, let's solve for ΔT based on your setup:
4800 J = (30 g)(0.34 J/g°C)(50°C - x)
Next, let's simplify the equation:
4800 J = 10.2 J/°C (50°C - x)
Now, distribute the 10.2 J/°C to both terms inside the parentheses:
4800 J = 510 J - 10.2 J/°C * x
Simplifying further:
4800 J - 510 J = -10.2 J/°C * x
4290 J = -10.2 J/°C * x
Now, divide both sides of the equation by -10.2 J/°C to isolate x:
4290 J / -10.2 J/°C = x
The units of joules cancel out, leaving:
-420 = x
So, based on your calculations, it appears that you made a sign error when dividing by -10.2 J/°C. The correct result should be x = -420°C, which means there was an error in the setup or calculation.
However, there seems to be another mistake when distributing the 10.2 J/°C in your calculations. Based on the given values, this is how the equation should be written:
4800 J = 10.2 J/g°C * (50°C - x) * 30 g
Now, let's distribute the 10.2 J/g°C to both terms inside the parentheses:
4800 J = 10.2 J/g°C * (50°C * 30g - x * 30g)
Simplifying further:
4800 J = 510 J * 30g - 10.2 J/g°C * 30g * x
Now, let's calculate the value inside the parentheses:
4800 J = 15300 J - 306 J/g°C * x * 30g
Subtract 15300 J from both sides of the equation:
-10500 J = -306 J/g°C * x * 30g
Now, cancel out the units of grams:
-10500 J = -9.18 J/°C * x
Finally, divide both sides of the equation by -9.18 J/°C to isolate x:
-10500 J / -9.18 J/°C = x
The units of joules cancel out:
1143.64 °C = x
Therefore, the initial temperature (x) is approximately 1143.64 °C.
The key takeaway here is to be careful with signs and always double-check your calculations to avoid errors.