Question

Two iron balls of different mass are heated to 100°C and dropped in water. If the same amount of heat is lost by the two balls to water, what can be said about the final temperatures of the two balls? (Heat lost = mCpΔT, where m = mass of the object, Cp = specific heat capacity of the material, and ΔT = change in temperature). A) Both balls will have the same temperature as the heat lost by both balls is the same. B) Both balls will have the same temperature as the specific heat capacities of both balls are the same. C) The lighter ball will have a higher temperature because the change of temperature is directly proportional to mass. D) The heavier ball will have a higher temperature because the change of temperature is inversely proportional to mass.

Answer 1

The correct option is D) The heavier ball will have a higher temperature because the change of temperature is inversely proportional to mass.

Step-by-step explanation:

The measurement and calculation of the amounts of heat exchanged by a body or system is called calorimetry.

In this way, there is a direct proportionality relationship between heat and temperature (Two magnitudes are directly proportional when there is a constant so that when one of the magnitudes increases, the other also; and the same occurs when either of them decreases .). The constant of proportionality depends on the substance that constitutes the body as its mass, and the product of specific heat results from the body's mass. So, the equation that allows you to calculate heat exchanges is:

Q = Cp * m * ΔT

Where Q is the heat exchanged in Joules for a body of mass m in grams, constituted by a specific heat substance Cp measured in joule per gram degree Celsius and where ΔT is the temperature variation measured in degree Celsius. The temperature variation is ΔT=Tfinal - Tinitical

Then the temperature variation will be:

ΔT=
`(Q)/(Cp*m)`

In this expression you can see that it follows the model of a rule of inverse proportionality
`y=(k)/(x)`. k is a constant that in this case is represented by Q and Cp. So, the change of temperature is inversely proportional to mass.

Finally the correct option is D) The heavier ball will have a higher temperature because the change of temperature is inversely proportional to mass.

Answer 2

The correct answer for this question is this one:"D) The heavier ball will have a higher temperature because the change of temperature is inversely proportional to mass."
Hope this helps answer your question and have a nice day ahead.