Thermodynamics

Step 1: Mean time between collisions is inversely proportional to number density and average speed:
Step 2: For an ideal gas,
Step 3: Hence,
Step 4: Therefore, Given:
Step 5: Substitute:
Step 6: Hence,

Step 1: Coordinates of charges and field point.
Step 2: Electric field due to a point charge:
Step 3: Field due to . Vector from to :
Step 4: Field due to . Vector from to :
Step 5: Resultant electric field: Expressing in required form:

Step 1: Convert pressure into SI units. Since,
Step 2: Use the ideal gas equation to find number of moles per unit volume.
Step 3: Convert moles into number of molecules per unit volume.
Step 4: Find the volume available per molecule.
Step 5: Estimate the mean distance between molecules. The mean separation is approximately the cube root of volume per molecule:
Hence, the correct answer is .

Step 1: Carnot cycle has two isotherms and two adiabats.
Step 2: Points on same isotherm have same temperature.
Step 3: From diagram A→B is isothermal; C→D is other isothermal.
Step 4: Therefore: Hence → (D).

Step 1: Use the principle of buoyancy. When the mass is removed, the cube rises, meaning the decrease in buoyant force equals the weight of the removed mass. Step 2: Write the relation. Loss of buoyant force weight of mass removed: where = area of the cube’s face, . Step 3: Cancel from both sides. Step 4: Substitute given values. Step 5: Find the side of the cube. Since the cube has a square face: Step 6: Final conclusion. The side of the cube is .

Step 1: Recall the basic property of waves. A wave is a disturbance that transfers energy from one place to another without transporting matter. Step 2: Analyze each option.

(A) Mass — not carried by waves
(B) Velocity — property of particles, not transported
(C) Wavelength — a characteristic of the wave, not something carried
(D) Energy — carried by waves ✔
Step 3: Final conclusion. Waves transfer energy from one place to another.