Step 1: State the First Law of Thermodynamics. The first law is often expressed as \( \Delta U = Q - W \), where \( \Delta U \) is the change in the internal energy of a system, \( Q \) is the heat added to the system, and \( W \) is the work done by the system.
Step 2: Interpret the meaning of the law. This law states that the change in a system's internal energy is equal to the heat supplied to the system minus the work done by the system. In essence, it says that energy cannot be created or destroyed, only transferred or changed from one form to another (e.g., from heat into work and internal energy).
Step 3: Relate the interpretation to fundamental conservation principles. The principle that energy cannot be created or destroyed is the law of conservation of energy. Therefore, the First Law of Thermodynamics is a restatement of the conservation of energy principle, specifically applied to thermodynamic systems.
If \(f(t)\) is the inverse Laplace transform of \( F(s) = \frac{s+1+s^{-2}}{s^2-1} \), then \(f(t)\) is
Match LIST-I with LIST-II
LIST-I (Differential Equation)
(A) \(\frac{dy}{dx} = 2x(y-x^2+1)\)
(B) \(x\frac{dy}{dx} + 2(x^2+1)y=6\)
(C) \((x^2+1)\frac{dy}{dx} + 2xy = x \sin x\)
(D) \(x^3\frac{dy}{dx} + 2xy = 2x^2e^{x^2}\)
LIST-II (Integrating Factor)
(I) \(x^2\)
(II) \(e^{-x^2}\)
(III) \(x^2e^x\)
(IV) \(1+x^2\)
Choose the correct answer from the options given below:
Match List - I with List - II
| List - I (Register) | List - II (Function) |
|---|---|
| A. Memory Address (MAR) | III. Holds address of the active memory location |
| B. Memory Buffer (MBR) | I. Holds information on its way to and from memory |
| C. Program Control (PC) | IV. Holds address of the next instruction to be executed |
| D. Accumulator (A) | II. Accumulates results and data to be operated upon |