Does Specific Heat Capacity Affect the Speed of Heat Transfer in Calorimeters?

[Pseudopro]

Homework Statement

This is a problem I made myself and it's really confusing me. You have 100mL of water and place it in a calorimeter of low specific heat capacity. You put another 100mL of water in another calorimeter of high specific heat capacity. Assume in both instances that the water is of a higher temperature than the calorimeters. Assume the water in both instances start at the same temperature. Assume the calorimeters start at the same temperature. They are closed systems. Will there be a difference in SPEED of heat energy transfer in each case.

Homework Equations

No calculations?

The Attempt at a Solution

While specific heat capacity tells us the relationship between heat energy and temperature, it doesn't seem to me to specify how fast the transfer is. I'm thinking right now that the heat energy transfer will be exactly the same for both instances. Only the calorimeter of higher shc will have a lower deltaT/t but heat transfer should be exactly the same?

 

[gneill]

While specific heat capacity tells us the relationship between heat energy and temperature, it doesn't seem to me to specify how fast the transfer is. I'm thinking right now that the heat energy transfer will be exactly the same for both instances. Only the calorimeter of higher shc will have a lower deltaT/t but heat transfer should be exactly the same?

Problems involving heat capacities and temperature differences often contain a phrase like "after a long time", or "when equilibrium is reached", in order to gloss over the dynamics of the heat exchange process. This occurs when the concepts being elucidated pertain to energy conservation and matter state transitions and such.

At some point you should come across problems that do worry about the actual rates of heat energy movement. They show up as scenarios with cooling or heating objects of various forms and in various ways, and Newton's Law of Cooling will appear.

Heat transfer is driven by temperature difference. Your low shc calorimeter will experience a greater change in temperature with less heat transferred to it than will the higher shc calorimeter. Once the temperature difference between the contents and the calorimeter has gone to zero, the heat transfer stops, too.

 

[Pseudopro]

Thanks gneill. When both heat transfers stop, will the lower shc setup have a higher temperature?

 

[gneill]

Thanks gneill. When both heat transfers stop, will the lower shc setup have a higher temperature?

It should. It takes less heat to raise its temperature, it it "steals' less heat from the source.

 

[rwisz]

You are correct in thinking that the specific heat capacity does not directly determine the speed of heat energy transfer. The specific heat capacity is a measure of the amount of heat energy required to raise the temperature of a substance by a certain amount. In this scenario, the speed of heat energy transfer will depend on other factors such as the thermal conductivity of the materials and the temperature difference between the water and the calorimeters. However, the specific heat capacity can indirectly affect the speed of heat transfer by influencing the temperature difference between the water and the calorimeters. The water in the calorimeter with a higher specific heat capacity will require more heat energy to raise its temperature to the same level as the water in the calorimeter with a lower specific heat capacity. This means that the temperature difference between the water and the calorimeter will be smaller in the former case, potentially resulting in a slower speed of heat energy transfer. Overall, the specific heat capacity is just one factor that can influence the speed of heat energy transfer, and other variables must be considered as well.