Chemistry and Chemical Reactivity (9th Edition)

a) The choice must be: heating the one with higher mass and specific heat capacity (1) and cooling the one with lowest mass and specific heat capacity (4). $100\ g\times 0.9002\ J/g.K \times(T-100)+$ $50\ g \times 0.1289\ J/g.K \times (T--10)+$ $300\ g\times4.184\ J/g.K\times (T-21)=0$; $90.02(T-100)+6.45(T+10)+$ $1255.20(T-21)=0$; $35297=1352T$; $T=26.1^{\circ}C$ b) For this to happen, the energies provided and removed by the metal pieces must cancel each other: $C_1(100-21)=C_2(21--10)$ $C_1/C_2=0.392$ Which is closest to heating 6 and cooling 2: $0.3860\times 50\div0.9002\div50=0.429$ $50\ g\times 0.3860\ J/g.K \times(T-100)+$ $50\ g \times 0.9002\ J/g.K \times (T--10)+$ $300\ g\times4.184\ J/g.K\times (T-21)=0$; $19.3(T-100)+45.1(T+10)+$ $1255.20(T-21)=0$; $27838.2=1319.5T$; $T=21.10^{\circ}C$