Question

If A vessel of thermal capacity 30 calories contains 170 g of water at 30 degree Celsius. If you drop a solid at 93 degree Celsius into the calorimeter, then the temperature of mixture becomes 33degree Celsius, find the thermal capacity of the solid.

Answer 1

in this question, we first see about the principle of calorimeter, which also explains the law of conservation of energy. From this principle we get the relation between the heat loss in the hot body and heat gained in the cold body. We will use this relation and use the given values to find the thermal capacity of the solid.
Formula used:
$\eta \times mass = \omega$
Heat lost by system= heat gained by the cold system

Complete answer:
Here, we can see the relation between heat capacity $\omega$ and $\eta$ specific heat capacity is given by:
$\eta \times mass = \omega$
Form the principle of calorimeter we have the relation:
Heat lost by hot body= heat gained by cold body, unless any amount of heat is lost to the surroundings.
Further, we have the relation: heat lost by solid is given by the product of change in temperature and heat capacity $\eta$ of solid
Heat gained by water and vessel is given by:
\eqalign{ & (33 - 30) \times \\{ (170 \times {\eta _w}) + {\omega _w}\\} = (93 - 33) \times {\omega _s} \cr & \Rightarrow 3 \times (170 + 30) = 60 \times {\omega _s} \cr & \therefore {\omega _s} = 10cal{/^ \circ }C \cr}
Therefore, the thermal capacity of solid is obtained in the above equation.

Additional information:
As we know that the thermal capacity is defined as the property of a material to absorb heat when the material is heated and to release heat when the material is cooled down.
Further, according to the principle of calorimeter the total heat lost by a hot body or material is equal to the total heat gained by the cold body or material. It can be written as Heat Lost is equal to Heat Gained. This principle is on the basis of the law of conservation of energy.
As we know that energy is defined as the ability to do work. Energy can be found in many things and can take different forms, like-kinetic energy is the energy of motion, and potential energy is energy due to an object's position or structure. Total energy of a system is given by the sum of kinetic energy and potential energy.
We also know that, according to the law of conservation of energy, energy can neither be created nor be destroyed; rather it can only be transferred from one form to another. Here, in this question electrical energy is transferred to heat energy.

Note:
We should remember that the laws of conservation of energy can never be violated in any case. According to the law of conservation of energy, energy can neither be created nor be destroyed; rather it can only be transferred from one form to another.