Calculate the amount of heat required to heat a 4.0kg gold bar from 20∘C to 61∘C. Specific heat capacity of gold is 0.128 J/g∘C.
How do we figure this out?
q = heat = mass x specific heat x (Tfinal-Tinitial)
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To calculate the amount of heat required to heat the gold bar, you can use the formula:
Q = mcΔT
Where:
Q is the amount of heat required (in Joules),
m is the mass of the gold bar (in kilograms),
c is the specific heat capacity of gold (in Joules per gram per degree Celsius), and
ΔT is the change in temperature (in degrees Celsius).
1. Convert the mass of the gold bar from kilograms to grams:
4.0 kg = 4000 g
2. Calculate the change in temperature:
ΔT = final temperature - initial temperature
ΔT = 61°C - 20°C
ΔT = 41°C
3. Substitute the values into the formula:
Q = (m)(c)(ΔT)
Q = (4000 g)(0.128 J/g∘C)(41°C)
4. Solve for the amount of heat required:
Q = 20768 J
Therefore, the amount of heat required to heat the 4.0 kg gold bar from 20°C to 61°C is 20768 Joules.
To calculate the amount of heat required to heat a substance, we can use the formula:
Q = m * c * ΔT
Where:
Q is the amount of heat (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity of the substance (in joules per gram per degree Celsius),
ΔT is the change in temperature (in degrees Celsius).
In this case, the mass of the gold bar is given as 4.0 kg, so we need to convert it to grams by multiplying by 1000:
m = 4.0 kg * 1000 g/kg
m = 4000 g
The specific heat capacity of gold is given as 0.128 J/g∘C.
The change in temperature, ΔT, is calculated by subtracting the initial temperature from the final temperature:
ΔT = 61 ∘C - 20 ∘C
ΔT = 41 ∘C
Now we can calculate the amount of heat (Q):
Q = m * c * ΔT
Q = 4000 g * 0.128 J/g∘C * 41 ∘C
Q = 20,480 J
Therefore, the amount of heat required to heat the 4.0 kg gold bar from 20∘C to 61∘C is 20,480 joules.