Question

Two metals of equal mass with different heat capacities are subjected to the same amount of heat. Which undergoes the smaller change in temperature (You must explain/justify your answer)? a) The metal with the higher heat capacity undergoes the smaller change in temperature. b) The metal with the lower heat capacity undergoes the smaller change in temperature. c) Both undergo the same change in temperature. d) You need to know the initial temperatures of the metals. e) You need to know which metals you have. Please explain why the answer is B.

Answer 1

I donot know how you got the answer as b) The metal with the lower heat capacity undergoes the smaller change in temperature. But in principle the correct answer is

a ) The metal with the higher heat capacity undergoes the smaller change in temperature.

Because

The heat capacity C of a material is defined to be the amount of heat Q it takes to raise the temperature of the material some small amount ΔTΔT.

C=Q / ΔT

(The specific heat is the heat capacity of the object divided by its mass, which is an immaterial difference for our purposes here).

A slightly more precise definition is the following: The heat capacity at constant volume of an object is

CV=∂U/∂T∣∣V

where U is the internal energy of the object, and derivative represents the change in internal energy of the object as temperature is increased but the volume is held fixed (there is also a heat capacity at constant pressure).

So heat gained = x J = specific heat capacity J/gC * mass g * (T final - T init)

for a specific value of x J / mass g, specific heat capacity and dT are INVERSELY related

a) The metal with the higher heat capacity undergoes the smaller change in temperature.

Is the correct answer