91Ó°ÊÓ

$30\mathrm{g}$of copper pellets at ${300}^{0}c$and $100ML$of water at ${20}^{0}c$

formula used:

The formula for calculating each element's energy is:$m\mathrm{Δ}{C}_p\mathrm{Δ}T$

Solving for $T_f$:

$$\begin{gathered} m_{\text{copper}}\mathrm{Δ}{C}_{p,\text{copper}}\mathrm{Δ}{T}_{i,\text{copper}}+m_{\text{water}}\mathrm{Δ}{C}_{p,\text{water}}\mathrm{Δ}{T}_{i,\text{water}} \\ =\left(m_{\text{copper}}\mathrm{Δ}{C}_{p,\text{copper}}+m_{\text{water}}\mathrm{Δ}{C}_{p,\text{water}}\right)\mathrm{Δ}{T}_f \\ {T}_f=\frac{m_{\text{copper}}\mathrm{Δ}{C}_{\text{peopper}}\mathrm{Δ}{T}_{\text{i, copper}}+m_{\text{wate}}\mathrm{Δ}{C}_{p,\text{watere}}\mathrm{Δ}{T}_{\text{i,water}}}{m_{\text{copper}}\mathrm{Δ}{C}_{\text{pcopper}}+m_{\text{water}}\mathrm{Δ}{C}_{p,\text{water}}} \end{gathered}$$

Now we need to figure out what kind of mass there is. $100ML$The water is $100[\mathrm{mL}]\mathrm{Δ}\frac{1|\mathrm{g}|}{1[\mathrm{mL}âˆ\pounds }=100[\mathrm{g}]$

The following information can be found in a table of specific heat capacity:

$C_{p,\text{copper}}=0.385\left[\frac{\mathrm{J}}{\mathrm{g}\mathrm{Δ}\mathrm{K}}\right]$

$C_{p,\text{water}}=4.1813\left[\frac{\mathrm{J}}{\mathrm{g}\mathrm{Δ}\mathrm{K}}\right]$

The initial temperature in Kelvin:

$$\begin{gathered} T_{i,\text{copper}}=300\left[{}^{∘}\mathrm{C}\right]+273.15=573.15[\mathrm{K}] \\ {T}_{i,\text{water}}=20\left[{}^{∘}\mathrm{C}\right]+273.15=293.15[\mathrm{K}] \end{gathered}$$

Substituting values:

$T_f=\frac{30|\mathrm{g}|\mathrm{Δ}0.385\left[\frac{\mathrm{J}}{8\mathrm{Δ}K}\right]\mathrm{Δ}573.15\left[K\right]+100|\mathrm{g}|\mathrm{Δ}4.181\left[\frac{\mathrm{J}}{g\mathrm{Δ}K}\right]\mathrm{Δ}293.15\left[K\right]}{30|\mathrm{g}|\mathrm{Δ}0.385\left[\frac{\mathrm{J}}{8\mathrm{Δ}K}\right]+100|\mathrm{g}|\mathrm{Δ}4.181\left[\frac{\mathrm{J}}{8\mathrm{Δ}K}\right]}$

$T_f=300.67\left[K\right]=27.52\left[{}^{∘}\mathrm{C}\right]$

The energy that the copper pellets lose is replaced by the energy gained by the water. There is no energy leakage into the environment because it is an isolated system.