The thermal energy balance equation for heat exchange is as follows (3 correct answers): eta =(Q_(1)-Q_(1oss))/(Q_(1))=(Q_(2))/(Q_(1)) Q_(1)=G_(1)c_(p1)(t_(1)'-t_(1)'')=G_(1)(h_(1)'-h_(1)'') D Q_(2)=Kcdot Fcdot Delta t D Q_(2)=G_(2)c_(p2)(t_(2)''-t_(2)')=G_(2)(h_(2)''-h_(2)') Q_(1)=G_(1)c_(p1)(t_(1)'-t_(1)'')cdot eta _(1)=G_(2)c_(p2)(t_(2)''-t_(2)') Q_(1)=W_(1)cdot delta t_(1)cdot eta =W_(2)cdot delta t_(2) Q_(1)-Q_(lows)=eta cdot Q_(1)=Q_(2)

The correct answers are:<br /><br />1. $\eta =\frac {Q_{1}-Q_{1oss}}{Q_{1}}=\frac {Q_{2}}{Q_{1}}$<br />2. $Q_{1}=G_{1}c_{p1}(t_{1}'-t_{1}'')=G_{1}(h_{1}'-h_{1}'')$<br />3. $Q_{2}=G_{2}c_{p2}(t_{2}''-t_{2}')=G_{2}(h_{2}h_{2}')$<br /><br />Explanation:<br /><br />1. The thermal energy balance equation $\eta =\frac {Q_{1}-Q_{1oss}}{Q_{1}}=\frac {Q_{2}}{Q_{1}}$ represents the efficiency of heat exchange, where $Q_{1}$ is the heat transferred to the first object, $Q_{1oss}$ is the heat loss, and $Q_{2}$ is the heat transferred to the second object.<br /><br />2. The equation $Q_{1}=G_{1}c_{p1}(t_{1}'-t_{1}'')=G_{1}(h_{1}'-h_{1}'')$ represents the heat transfer to the first object, where $G_{1}$ is the mass flow rate, $c_{p1}$ is the specific heat capacity of the first object, and $(t_{1}'-t_{1}'')$ and $(h_{1}'-h_{1}'')$ are the temperature and enthalpy changes of the first object.<br /><br />3. The equation $Q_{2}=G_{2}c_{p2}(t_{2}''-t_{2}')=G_{2}(h_{2}''-h_{2}')$ represents the heat transfer to the second object, where $G_{2}$ is the mass flow rate, $c_{p2}$ is the specific heat capacity of the second object, and $(t_{2}''-t_{2}')$ and $(h_{2}''-h_{2}')$ are the temperature and enthalpy changes of the second object.