Estimate the increase in rest energy of a copper sample
[100 kg, c = 387 J/(kg · °C)]
if its temperature is increased 100°C.
-answer needs to be in kg please.
To estimate the increase in rest energy of a copper sample, we need to use the formula for change in internal energy.
The formula for change in internal energy is given as:
ΔU = mcΔT
where ΔU is the change in internal energy, m is the mass of the sample, c is the specific heat capacity of the material, and ΔT is the change in temperature.
First, let's calculate the change in internal energy using the given values:
Mass of the copper sample (m) = 100 kg
Specific heat capacity of copper (c) = 387 J/(kg · °C)
Change in temperature (ΔT) = 100 °C
Using the formula ΔU = mcΔT, we can calculate the change in internal energy:
ΔU = (100 kg) * (387 J/(kg · °C)) * (100 °C)
= 3870000 J
Now, the change in energy is expressed in joules. To convert it to kilograms, we need to use Einstein's mass-energy equivalence equation:
E = mc^2
Rearranging the equation, we have:
m = E / c^2
where E is the energy, m is the mass, and c is the speed of light (approximately 3x10^8 m/s).
Let's calculate the change in mass using the formula m = E / c^2:
m = 3870000 J / (3x10^8 m/s)^2
= 4.3 * 10^-8 kg
Therefore, the estimated increase in rest energy of the copper sample is approximately 4.3 * 10^-8 kg.