Answer to Question #162583 in Physics for maryjoy

Question

A 55-g copper calorimeter contains 250 g of water at 18oC. When 75 g of an alloy at 100oC is dropped into the calorimeter, the resulting temperature is 20.4oC. What is the specific heat of the alloy?

Answer 1

The copper calorimeter and water will heated while alloy will cooled. We can write the heat balance equation:

$$m_cc_c(T_f-T_w)+m_wc_w(T_f-T_w)=m_{alloy}c_{alloy}(T_{alloy}-T_f),$$ $$c_{alloy}=\dfrac{m_cc_c(T_f-T_w)+m_wc_w(T_f-T_w)}{m_{alloy}(T_{alloy}-T_f)},$$

$c_{alloy}=\dfrac{0.55\ kg\cdot390\ \dfrac{J}{kg\cdot \!^{\circ}C}\cdot(20.4^{\circ}C-18^{\circ}C)+0.25\ kg\cdot4184\ \dfrac{J}{kg\cdot \!^{\circ}C}\cdot(20.4^{\circ}C-18^{\circ}C)}{0.75\ kg \cdot(100^{\circ}C-20.4^{\circ}C)},$

$$c_{alloy}=50.67\ \dfrac{J}{kg\cdot \!^{\circ}C}.$$