Jawaharlal Nehru Technological University Hyderabad B.Tech II MATERIALS THERMODYNAMICS Previous Question Paper (March - 2022 - R18)

Internal energy (U) is the total microscopic energy contained within a system, representing the sum of the kinetic and potential energies of all its constituent molecules, atoms, and subatomic particles. It is a state function, meaning it depends only on the current state of the system and not on the path taken to reach it.

The First Law of Thermodynamics, which is the principle of conservation of energy, states that energy cannot be created or destroyed, only transformed. It relates internal energy to heat (Q) and work (W) through the energy balance equation:

In this expression, ΔU represents the change in internal energy, Q is the heat added to the system, and W is the work done by the system. This law dictates that any energy entering or leaving a closed system must manifest as a change in the internal energy of the system, effectively linking the macroscopic exchange of energy (heat and work) to the microscopic state of the matter.

For an adiabatic process, the heat transfer is zero by definition:

To calculate the work required for an adiabatic compression of an ideal gas, we use the relation for work done on the system:

Given: m = 4.0 kg, P₁ = 1 bar, T₁ = 298 K, P₂ = 15 bar. Assuming air as an ideal gas with γ = 1.4 and C_v = 0.718 kJ/kg·K.

1. Determine final temperature T₂ using the adiabatic relation: T₂ = T₁ × (P₂/P₁)^((γ-1)/γ)
2. T₂ = 298 × (15/1)^(0.4/1.4) = 298 × 2.44 = 727.12 K
3. Calculate work: W = 4.0 × 0.718 × (298 - 727.12)
4. W = 2.872 × (-429.12) = -1232.43 kJ

The negative sign indicates that work is done on the system. Thus, the work required is 1232.43 kJ.