解:已知金属块的质量$m = 500\ \text{g} = 0.5\ \text{kg},$初温$t_0 = 80^\circ\text{C},$末温$t = 30^\circ\text{C},$放出的热量$Q_{\text{放}}=2.2\times10^{4}\ \text{J}。$
温度变化量$\Delta t=t_0 - t=80^\circ\text{C}-30^\circ\text{C}=50^\circ\text{C}。$
根据放热公式$Q_{\text{放}}=cm\Delta t,$可得比热容$c=\frac{Q_{\text{放}}}{m\Delta t}。$
将数值代入得:$c=\frac{2.2\times10^{4}\ \text{J}}{0.5\ \text{kg}\times50^\circ\text{C}}=\frac{2.2\times10^{4}\ \text{J}}{25\ \text{kg}\cdot^\circ\text{C}} = 8.8\times10^{2}\ \text{J}/(\text{kg}\cdot^\circ\text{C})。$
答:这种金属的比热容是$8.8\times10^{2}\ \text{J}/(\text{kg}\cdot^\circ\text{C})。$