The water equivalent of a calorimeter is $10\, g$ and it contains $50 \,g$ of water at $15�C$. Some amount of ice, initially at $-10�C$ is dropped in it and half of the ice melts till equilibrium is reached. What was the initial amount of ice that was dropped (when specific heat of ice $= 0.5 \,cal\, gm^{-1}�C^{-1},$ specific heat of water $= 1.0 \,cal\, gm^{-1}�C^{-1}$ and latent heat of melting of ice $= 80 \,cal \,gm^{-1}$) ?
- 10 g
- 18 g
- 20 g
- 30 g
The Correct Option is C
Solution and Explanation
Applying calorimetry principle,
heat given $=$ heat taken
$\left(m_{1}+m_{2}\right) s_{1}\left(t_{1}-t\right)=\frac{m L}{2}+m s_{2}\left(t-t_{2}\right)$
Putting values, we get
$(10+50) \times 1 \times(15-0)=\frac{m}{2} \times 80+m \times 0.5[0-(-10)]$
$\Rightarrow 60 \times 15=40 m+\frac{m}{2} \times 10=45\, m$
$\therefore m=\frac{60 \times 15}{45}=20\, g$
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Concepts Used:
Calorimetry
In chemistry and thermodynamics, calorimetry is the science or act of measuring changes in state variables of a body for the purpose of deriving the heat transfer associated with changes of its state due, for example, to chemical reactions, physical changes, or phase transitions under specified constraints. Calorimetry is performed with a calorimeter. Scottish physician and scientist Joseph Black, who was the first to recognize the distinction between heat and temperature, is said to be the founder of the science of calorimetry.
Calorimeter Principle
When two bodies of different temperatures (preferably a solid and a liquid) are placed in physical contact with each other, the heat is transferred from the body with higher temperature to the body with lower temperature until thermal equilibrium is attained between them. The body at higher temperature releases heat while the body at lower temperature absorbs heat. The principle of calorimetry indicates the law of conservation energy, i.e. the total heat lost by the hot body is equal to the total heat gained by the cold body.
The heat transfer in a system is calculated using the formula,
Heat Lost = Heat Gained
Where
q is the measure of heat transfer
m is the mass of the body
c is the specific heat of the body
Δt is the change in the temperature