Calculate the amount of heat required to heat a 3.6{\rm kg} gold bar from 20^\circ {\rm C} to 70^\circ {\rm C}. Specific heat capacity of gold is 0.128 \rm J/g ^\circ C
q = mass x specific heat x (Tfinal-Tinitial)
To calculate the amount of heat required to heat the gold bar, we can use the formula:
Q = m * c * ΔT
Where:
Q = amount of heat (in Joules)
m = mass of the gold bar (in kg)
c = specific heat capacity of gold (in J/g °C)
ΔT = change in temperature (in °C)
First, let's convert the mass from kg to grams:
m = 3.6 kg * 1000 g/kg = 3600 g
Now, we can plug in the values into the formula:
Q = 3600 g * 0.128 J/(g °C) * (70 °C - 20 °C)
To simplify the calculation, let's first subtract the temperatures:
ΔT = 70 °C - 20 °C = 50 °C
Now we can continue with the calculation:
Q = 3600 g * 0.128 J/(g °C) * 50 °C
We can cancel out the unit g (grams) from the numerators and denominators:
Q = 3600 * 0.128 J/°C * 50 °C
Now we can multiply the numbers together to find the answer:
Q = 23,040 J
Therefore, the amount of heat required to heat the 3.6 kg gold bar from 20°C to 70°C is 23,040 Joules.