Calculate the amount of heat required to heat a 3.7{\rm kg} gold bar from 30^\circ {\rm C} to 61^\circ {\rm C}. Specific heat capacity of gold is 0.128 \rm J/g ^\circ C
q = mass Au x specific heat Au x (Tfinal-Tinitial)
Make sure mass and specif heat are in the same unit. 3.7 kg = 3700 g
To calculate the amount of heat required to heat the gold bar, you can use the formula:
Q = m * c * ΔT
Where:
Q is the amount of heat transferred (in joules),
m is the mass of the object (in kilograms),
c is the specific heat capacity of the material (in joules per gram per degree Celsius),
ΔT is the change in temperature (in degrees Celsius).
First, you need to convert the mass of the gold bar from grams to kilograms. Since 1 kg equals 1000 grams:
m = 3.7 kg * 1000 g/kg
m = 3700 g
Next, you can substitute the values into the formula:
Q = 3700 g * 0.128 J/g°C * (61°C - 30°C)
Now, we need to account for the unit conversion from grams to kilograms:
Q = 3700 g * 0.128 J/g°C * 31°C
Calculate the value:
Q = 1501.6 J/g°C * 31°C
Finally, calculate the total amount of heat:
Q = 46,548.8 J
Therefore, the amount of heat required to heat the 3.7 kg gold bar from 30°C to 61°C is approximately 46,548.8 joules.