Question

Solution A has a specific heat of 2.0 J/g◦C. Solution B has a specific heat of 3.8 J/g◦C. If equal masses of both solutions start at the same temperature and equal amounts of heat are added to each solution, which will be true? 1. SolutionBattainsahigher temperature. 2. Solution A attains a higher temperature. 3. Both solutions have the same final temperature.

Answer 1

Answer: 2. Solution A attains a higher temperature.

Explanation: Specific heat simply means, that amount of heat which is when supplied to a unit mass of a substance will raise its temperature by 1°C.

In the given situation we have equal masses of two solutions A & B, out of which A has lower specific heat which means that a unit mass of solution A requires lesser energy to raise its temperature by 1°C than the solution B.

Since, the masses of both the solutions are same and equal heat is supplied to both, the proportional condition will follow.

We have a formula for such condition,

$Q=m.c.\Delta T$.....................................(1)

where:

• $\Delta T$= temperature difference

• Q= heat energy

• m= mass of the body

• c= specific heat of the body

Proving mathematically:

According to the given conditions

• we have equal masses of two solutions A & B, i.e. $m_A=m_B$

• equal heat is supplied to both the solutions, i.e. $Q_A=Q_B$

• specific heat of solution A, $c_{A}=2.0 J.g^{-1} .\degree C^{-1}$

• specific heat of solution B, $c_{B}=3.8 J.g^{-1} .\degree C^{-1}$

• $\Delta T_A$ & $\Delta T_B$ are the change in temperatures of the respective solutions.

Now, putting the above values

$Q_A=Q_B$

$m_A.c_A. \Delta T_A=m_B.c_B . \Delta T_B\\\\2.0\times \Delta T_A=3.8 \times \Delta T_B\\\\ \Delta T_A=\frac{3.8}{2.0}\times \Delta T_B\\\\\\\frac{\Delta T_{A}}{\Delta T_{B}} = \frac{3.8}{2.0}>1$

Which proves that solution A attains a higher temperature than solution B.