Respuesta :
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,
[tex]Q=m.c.\Delta T[/tex].....................................(1)
where:
- [tex]\Delta T[/tex]= 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. [tex]m_A=m_B[/tex]
- equal heat is supplied to both the solutions, i.e. [tex]Q_A=Q_B[/tex]
- specific heat of solution A, [tex]c_{A}=2.0 J.g^{-1} .\degree C^{-1}[/tex]
- specific heat of solution B, [tex]c_{B}=3.8 J.g^{-1} .\degree C^{-1}[/tex]
- [tex]\Delta T_A[/tex] & [tex]\Delta T_B[/tex] are the change in temperatures of the respective solutions.
Now, putting the above values
[tex]Q_A=Q_B[/tex]
[tex]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[/tex]
Which proves that solution A attains a higher temperature than solution B.
