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* \Delta T_A=3.8 * \Delta T_B\\\\ \Delta T_A=(3.8)/(2.0)* \Delta T_B\\\\\\(\Delta T_(A))/(\Delta T_(B)) = (3.8)/(2.0)>1`

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