Govt. Exams
For isochoric process (constant volume): PV = nRT with V constant gives P/T = nR/V = constant (Gay-Lussac's Law)
Mayer's relation: Cₚ - Cᵥ = R for one mole of ideal gas, hence Cₚ = Cᵥ + R
For an ideal gas, internal energy U depends only on temperature (U = nCᵥT), not on pressure or volume independently
The first law states: ΔU = Q + W, where ΔU is change in internal energy, Q is heat absorbed, and W is work done on the system
Carnot efficiency: η = 1 - (Tc/Th) = 1 - (300/500) = 1 - 0.60 = 0.40 or 40%
N - mg = ma (upward acceleration), so N = m(g + a) = 60(10 + 2) = 60 × 12 = 720 N
Centripetal force F = ma_c = 2 × 8 = 16 N. This is the net force directed toward the center of circular motion.
At 45°, vertical component = 20sin(45°) = 10√2 m/s. Using v² = u² - 2gh, at max height v=0: h = u²/(2g) = (10√2)²/(2×10) = 200/20 = 10 m
Maximum velocity in SHM = ωA = 4 × 0.5 = 2 m/s
Net force = (3-3)i + (4-4)j = 0i + 0j = 0 N. The magnitude is 0 N.
