Question

Assertion
The specific heat of a gas in an adiabatic process is zero but it is infinite in an isothermal process.
Reason
Specific heat of a gas is directly proportional to heat exchange with the system and inversely proportional to change in temperature.
(A) Statement-1 is false. Statement-2 is true.
(B) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
(C) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(D) Statement-1 is true, Statement-2 is false

Answer 1

Hint: We know that thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In particular, it describes how thermal energy is converted to and from other forms of energy and how it affects matter. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes. With these tools, thermodynamics can be used to describe how systems respond to changes in their environment. Based on this concept we have to solve this question.

Complete step by step answer
Specific heat is defined as the amount of energy required to raise the temperature of 1 kg of a substance by $1^{\circ }\mathrm{C}$.
The formula is given by:
$C={\displaystyle \frac{Q}{m\mathrm{\Delta }T}}$
We can say that an isothermal process is a thermodynamic process in which the temperature of a system remains constant. The transfer of heat into or out of the system happens so slowly that thermal equilibrium is maintained. In general, during an isothermal process there is a change in internal energy, heat energy, and work, even though the temperature remains the same. Something in the system works to maintain that equal temperature.
In the isothermal process $\mathrm{\Delta }\mathrm{T}=0.$ Therefore, $\mathrm{C}$ is infinite.
We know that an adiabatic process occurs without transferring heat or mass between a thermodynamic system and its surroundings. Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as work. An adiabatic process has a change in temperature but no heat flow. The isothermal process has no change in temperature but has heat flow.
In adiabatic process $\mathrm{Q}=0.$ Therefore, $\mathrm{C}$ is zero.
Thus, we can say that Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Hence the correct option is option B.

Note: There are three laws of thermodynamics that are required to be known. The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. The Second Law of Thermodynamics says that processes that involve the transfer or conversion of heat energy are irreversible. The laws of thermodynamics describe the relationships between thermal energy, or heat, and other forms of energy, and how energy affects matter. The third law of thermodynamics states that the entropy of a system at absolute zero is a well-defined constant. This is because a system at zero temperature exists in its ground state, so that its entropy is determined only by the degeneracy of the ground state.