Step 1: Understand phase changes and energy.
Changing the phase of a substance requires an input or release of energy, known as latent heat.
- Melting (solid to liquid) and evaporation (liquid to gas) are endothermic processes; they absorb heat from the surroundings, causing cooling.
- Freezing (liquid to solid) and condensation (gas to liquid) are exothermic processes; they release heat into the surroundings, causing warming.
Step 2: Apply this to condensation.
When water vapor (a gas) condenses into liquid water droplets to form clouds, it must release the energy that was required to turn it into a gas in the first place. This released energy is called the latent heat of condensation. This energy is transferred to the surrounding air molecules.
Conclusion: The release of latent heat during condensation warms the surrounding atmosphere. This is a crucial process in the development of storms like hurricanes.
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: