Question

Energy is transferred as the heat between two objects, one with a temperature of 5 C and the other with a temperature of 20 C. If two other objects are to have the same amount of energy transferred between them, what might their temperatures be?

Answer 1

Answer:

Final temperature is located between 5 °C and 20 °C.

Explanation:

The object with high temperature transfers energy to the object with low temperature until thermal equilibrium is reached, that is, when both objects have the same temperature.

$Q_{H} = -Q_{L}$

$C_{H}\cdot (20^{\textdegree}C - T) = -C_{L}\cdot (5^{\textdegree}C-T)$

$20\cdot C_{H} - C_{H}\cdot T = -5\cdot C_{L}+ C_{L}\cdot T$

$(C_{H}+C_{L})\cdot T=20\cdot C_{H} + 5\cdot C_{L}$

$T = 20\cdot\frac{C_{H}}{C_{L}+C_{H}} + 5\cdot \frac{C_{L}}{C_{L}+C_{H}}$

Now, let consider three scenarios:

Scenario 1 - $C_{H} = C_{L]$

$T = 12.5^{\textdegree}C$

Scenario 2 - $C_{H}>> C_{L}$

$T = 20^{\textdegree}C$

Scenario 3 - $C_{H}$

$T = 5^{\textdegree}C$

Final temperature is located between 5 °C and 20 °C.