In three experiments, a material A at a particular low temperature T C and a material B at a particular high temperature T H are placed in a isolated and insulated container. When they reach therm

Question

In three experiments, a material A at a particular low temperature $T_{C}$ and a material B at a particular high temperature $T_{H}$ are placed in a isolated and insulated container. When they reach thermal equilibrium with each other (No phase change occurs), their final temperature $T_{f}$ is measured. The masses $m_{A}$ & $m_{B}$ and specific heats $C_{A}$ & $C_{B}$ of the materials are given in the table. Assume that heat transferred is $Q$ in the experiment.

Experiment	$m_{A}$	$C_{A}$	$m_{B}$	$C_{B}$
1	$m$	$c$	$m$	$c$
2	$m$	$c$	$2 m$	$c$
3	$m$	$2 c$	$m$	$c$

Then which of the following is correct

TestHub · Accepted Answer

The final temperature is the heat-capacity-weighted mean:
$T_{f} = \frac{( m c ) _{A} T _{C} + ( m c ) _{B} T _{H}}{( m c ) _{A} + ( m c ) _{B}}$
$(T_{f})_{1} = \frac{T _{C} + T _{H}}{2}$
$(T_{f})_{2} = \frac{T _{C} + 2 T _{H}}{3}$
$(T_{f})_{3} = \frac{2 T _{C} + T _{H}}{3}$
Experiment 2 has the larger heat capacity on the hot side, and experiment 3 on the cold side.
$(T_{f})_{2} > (T_{f})_{1} > (T_{f})_{3}$

Physics - Heat & Thermo Question with Solution | TestHub

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