Respuesta :
The absorbed or released by a system is given by the following formula:
[tex]Q=m\cdot Cp\cdot\Delta T[/tex]Where Q is the heat absorbed or released, m is the mass of the system, Cp is the specific heat and ΔT is the change in the temperature.
Let mA and mB be the mass of objects A and B, let CpA and CpB be the specific heats of objects A and B and let ΔTA and ΔTB be the specific heats of objects A and B. We will have that:
[tex]\begin{gathered} mA=3mB \\ CpA=2CpB \end{gathered}[/tex]If the same amount of heat is applied to both object, we will have that:
[tex]\begin{gathered} QA=QB \\ mA\cdot CpA\cdot\Delta TA=mB\cdot CpB\cdot\Delta TB \end{gathered}[/tex]Replace mA and CpA for their equivalences in terms of mB and CpB:
[tex]\begin{gathered} 3mB\cdot2CpB\cdot\Delta TA=mB\cdot CpB\cdot\Delta TB \\ \Delta TA=\frac{mB}{3mB}\cdot\frac{CpB}{2CpB}\cdot\Delta TB \\ \Delta TA=\frac{1}{3}\cdot\frac{1}{2}\Delta TB \\ \Delta TA=\frac{1}{6}\Delta TB \end{gathered}[/tex]It means that the change in temperature of A is 1/6 of the change of temperature of B.
[tex]\Delta TA=\frac{1}{6}\Delta TB[/tex]