Question

Substances A and B, initially at different temperatures, come in contact with each other and reach
thermal equilibrium. The mass of substance A is twice the mass of substance B. The specifi c
heat capacity of substance B is twice the specifi c heat capacity of substance A. Which statement
is true about the fi nal temperature of the two substances once thermal equilibrium is reached?
(a) The fi nal temperature will be closer to the initial temperature of substance A than substance B.
(b) The fi nal temperature will be closer to the initial temperature of substance B than substance A.
(c) The fi nal temperature will be exactly midway between the initial temperatures of substances
A and B.

Answer 1

If you have trouble with a problem like this with "reasoning it out", I suggest you assign numbers. Perhaps something like this.
Say A = 100 g and is twice B which makes B 50 g. Check that.

Specific heat A = 1. B is 2x A so B is 2. Check that.

Initial T A = 100; initial B = 50

[mass A x specific heat A x (Tfinal-Tinital)] + [mass B x specific heat B x (Tfinal-Tinitial)] = 0
Solve for Tfinal and check that against the answers.

Then the fun of it change Tinitial for A = 50 and Tinitial B is 100. See if your conclusion is the same for either setting.