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 specific heat capacity of substance B is twice the specific heat capacity of substance A.
Which statement is true about the final temperature of the two substances once thermal equilibrium is reached?1) The final temperature will be closer to the initial temperature of substance B than substance A.2) The final temperature will be exactly midway between the initial temperatures of substances A and B.3) The final temperature will be closer to the initial temperature of substance A than substance B.

Answer 1

Answer: .2) The final temperature will be exactly midway between the initial temperatures of substances A and B.

Explanation:

$heat_{absorbed}=heat_{released}$

As we know that,  

$Q=m\times c\times \Delta T=m\times c\times (T_{final}-T_{initial})$

$m_A\times c_A\times (T_{final}-T_A)=-[m_B\times c_B\times (T_{final}-T_2)]$         .................(1)

where,  

q = heat absorbed or released

$m_A$ = mass of A = 2x

$m_B$ = mass of B = x

$T_{final}$ = final temperature = z

$T_A$ = temperature of A

$T_2$ = temperature of B

$c_A$ = specific heat capacity of A = y

$c_B$ = specific heat capacity of B = 2y

Now put all the given values in equation (1), we get

$2x\times y\times (z-T_A)=-[x\times 2y\times (z-T_B)]$

$2z=T_B+T_A$

$z=\frac{T_B+T_A}{2}$

Therefore, the final temperature of the mixture will be exactly midway between the initial temperatures of substances A and B.