91Ó°ÊÓ

The diameter of the sphere is $6.0\mathrm{cm}$and the temperature goes from $-50°\mathrm{C}$to $150°\mathrm{C}$.

The heat energy can be calculated with the heat capacity equation:

$Q=m\mathrm{Δ}{C}_p\mathrm{Δ}\mathrm{Δ}T$

Where $m$is the mass, $C_p$is the specific heat and $\mathrm{Δ}T$is the difference of temperature in the object. The change of heat energy is positive when the temperature increase and negative if otherwise. To calculate the mass of the sphere:

$m=V\mathrm{Δ}\mathrm{ÒÏ}$

Where $V$is the volume and $\mathrm{ÒÏ}$is density.

Calculation:

First, we need to know how much mass of copper we have; from copper property tables we find its density:

$\mathrm{ÒÏ}=8960\left[\frac{\mathrm{kg}}{{\mathrm{m}}^3}\right]$

Substituting values:

$m=\frac{4}{3}\mathrm{π}(0.03[\mathrm{m}]{)}^3\mathrm{Δ}8960\left[\frac{\mathrm{kg}}{{\mathrm{m}}^3}\right]=1.01[\mathrm{kg}]$

The specific heat of copper:

$C_p=0.385\left[\frac{kJ}{kg{\mathrm{Δ}}^{D}C}\right]$

Solving for $Q$:

$Q=1.01[\mathrm{kg}]\mathrm{Δ}0.385\left[\frac{\mathrm{kJ}}{k_g\mathrm{Δ}°\mathrm{C}}\right]\mathrm{Δ}\left(150\left[{}^{∘}\mathrm{C}\right]-\left(-50\left[{}^{∘}\mathrm{C}\right]\right)\right)=77.77\left[kJ\right]$