Objects A and B both have mass 2 kg. Object A has temperature 20°C and Object B has temperature 40°C. The specific heat of Object A is larger than that of Object B. The two objects are isolated from the environment and are brought into thermal contact with each other and allowed to come to thermal equilibrium. Is the final temperature of both objects greater than, less than or equal to 30°C? Briefly explain your reasoning.

Answer:

Equal to 30°C.

Explanation:

The final temperature of both objects are equal to 30°C because of the conduction heat from one object to another. Both objects have same mass of 2 kg and both were isolated from the external environment so conduction of heat occurs from the more hotter body to the less hotter body until the temperature of both objects are equal to each other.

The final temperature of both objects is less than 30° C

The specific heat of an object is the minimum required quantity of heat needed to raise the temperature of 1 gram of the object(substance) by 1° C.

From the parameters given:

Using the Calorimetry principle, we need to understand that the heat lost by an object at a high temperature is proportionally equal to that heat gained by the object at a low temperature.

i.e.

[tex]\mathbf{Q_{lost}= Q_{gain}}[/tex]

[tex]\mathbf{ms_B \Big[40^0 \ C - \theta_o\Big]= ms_A \Big [ \theta_o - 20^0 \ C \Big]}[/tex]

Given that:

Then, let us consider a scenario where [tex]\mathbf{S_A = 1.5S_B}[/tex]

Thus;

[tex]\mathbf{S_B \Big[40^0 \ C - \theta_o\Big]= 1.5S_B \Big [ \theta_o - 20^0 \ C \Big]}[/tex]

[tex]\mathbf{40^0 \ C - \theta_o= 1.5 \theta_o - 20^0 \ C}[/tex]

[tex]\mathbf{ 2.5\theta_o= 70^0 \ C}[/tex]

[tex]\mathbf{ \theta_o= \dfrac{70^0 \ C}{2.5}}[/tex]

[tex]\mathbf{ \theta_o=28 ^0 C}[/tex]

Therefore, we can conclude that since the specific heat of object A is larger than that of object B i.e. [tex]\mathbf{S_A> S_B}[/tex], then the final temperature [tex]\mathbf{ \theta_o<30 ^0 C}[/tex]

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