Calculate the amount of heat required to heat a 3.5 kg gold bar from 21 degrees C to 37 degrees C. What would be the best way to work this problem? I don't know if I need to convert the kg to g.
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To calculate the amount of heat required to heat a gold bar, you will need to use the equation:
Q = mcΔT
Where:
Q is the amount of heat (in Joules) required
m is the mass of the gold bar (in kilograms)
c is the specific heat capacity of gold (in Joules per kilogram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)
First, let's determine if you need to convert the mass from kilograms to grams. The specific heat capacity is usually given in Joules per gram per degree Celsius, so it would be convenient to have the mass in grams. However, in your case, the mass is already in kilograms, which means you don't need to convert it.
Now, let's determine the specific heat capacity of gold. The specific heat capacity of gold is approximately 0.129 J/g°C. Since we're working with kilograms, we need to convert it to Joules per kilogram per degree Celsius. This can be done by dividing the specific heat capacity by 1000:
c = 0.129 J/g°C ÷ 1000 = 0.000129 J/kg°C
Now, substitute the values into the equation:
Q = (3.5 kg) (0.000129 J/kg°C) (37°C - 21°C)
Q = (3.5 kg) (0.000129 J/kg°C) (16°C)
The units cancel out, and you're left with:
Q = 0.0007212 J
Therefore, the amount of heat required to heat the gold bar from 21°C to 37°C is approximately 0.0007212 Joules.