Which thermodynamic process results in maximum work extraction from an ideal gas expanding from the same initial to final states?
Answer: B
For expansion between the same P-V states, isothermal process produces maximum work because W = nRT ln(V_f/V_i) is maximum when temperature is highest throughout the process.
Q.182Easy
A heat engine operates between two reservoirs at temperatures 500 K and 300 K. What is the maximum theoretical efficiency of this engine?
A gas expands isothermally from volume V₁ to 3V₁ at temperature T. If the initial pressure is P₁, what is the work done by the gas?
Answer: A
For isothermal process: W = nRT ln(V_f/V_i) = P₁V₁ ln(3V₁/V₁) = P₁V₁ ln(3)
Q.185Medium
A system undergoes a cyclic process. The internal energy change over one complete cycle is ΔU. Which statement is correct?
Answer: A
Internal energy is a state function, so for a cyclic process where the system returns to its initial state, ΔU = 0 always, regardless of the path.
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Q.186Medium
Two identical blocks at different temperatures are brought into thermal contact in an isolated system. Block A at 400 K and Block B at 300 K both have mass 1 kg and specific heat 400 J/kg·K. What is the change in entropy of the universe?
An ideal gas undergoes an adiabatic process from state (P₁, V₁, T₁) to (P₂, V₂, T₂) with γ = 1.4. If volume increases by 50%, the temperature ratio T₂/T₁ is approximately:
A refrigerator operates with a COP (Coefficient of Performance) of 4 between temperatures 250 K and 350 K. What is the theoretical maximum COP possible?
A 2 kg mass of ice at 0°C is mixed with 5 kg of water at 80°C in a thermally insulated container. If latent heat of fusion = 3.36 × 10⁵ J/kg and specific heat of water = 4200 J/kg·K, determine the final state of the system.
Answer: A
Heat available from water cooling from 80°C to 0°C: Q = 5 × 4200 × 80 = 1.68 × 10⁶ J. Heat needed to melt ice: Q = 2 × 3.36 × 10⁵ = 6.72 × 10⁵ J. Since 1.68 × 10⁶ > 6.72 × 10⁵, all ice melts. Remaining heat: 1.68 × 10⁶ - 6.72 × 10⁵ = 1.008 × 10⁶ J raises temperature of 7 kg water: ΔT = 1.008 × 10⁶/(7 × 4200) ≈ 34.3°C → final temp ≈ 34°C
Q.190Hard
A gas sample undergoes a process where pressure decreases linearly with volume: P = P₀ - kV, where k is a constant. For 1 mole of ideal gas at constant temperature, what is the work done when volume changes from V₁ to V₂?
Answer: A
Work done: W = ∫P dV = ∫(P₀ - kV) dV from V₁ to V₂ = [P₀V - kV²/2] from V₁ to V₂ = P₀(V₂ - V₁) - k(V₂² - V₁²)/2
Q.191Easy
Two point charges of +2 μC and -2 μC are placed 10 cm apart. What is the electric field at a point midway between them?
Answer: A
For a dipole configuration, the electric field at the midpoint is E = 2kq/r² directed from negative to positive charge. E = 2 × 9 × 10⁹ × 2 × 10⁻⁶ / (0.05)² = 7.2 × 10⁶ N/C
Q.192Easy
The electric potential due to a point charge is V = kq/r. If the charge is doubled and distance is halved, the potential becomes:
Answer: B
V' = k(2q)/(r/2) = 4kq/r = 4V. Doubling charge increases V by 2×, halving distance increases V by 2×, total effect is 4×
Q.193Easy
A conducting sphere of radius 10 cm carries a charge of 5 μC. The electric field at a distance of 5 cm from the center inside the conductor is:
Answer: A
Inside a conductor in electrostatic equilibrium, the electric field is always zero regardless of position or charge distribution
Q.194Easy
A parallel plate capacitor has plates of area A separated by distance d. If a dielectric of constant K is inserted between the plates, the capacitance becomes:
Answer: B
Capacitance with dielectric: C = Kε₀A/d, where K is the dielectric constant. The dielectric increases capacitance by a factor of K
Q.195Medium
Three identical charges q are placed at the vertices of an equilateral triangle of side a. The electric potential at the centroid is:
Answer: A
Distance from each vertex to centroid = a/√3. Total potential = 3 × kq/(a/√3) = 3√3kq/a. Correction: V = 3kq√3/a ≈ 3kq/a for approximation
Q.196Medium
A uniformly charged infinite plane sheet has surface charge density σ. The electric field due to the sheet is:
Answer: A
Using Gauss's law for an infinite plane sheet: E = σ/(2ε₀). The field is independent of distance and uniform on both sides
Q.197Hard
A charged soap bubble of radius R has surface charge density σ. The excess pressure inside the bubble due to electrostatic force is:
Answer: A
Electrostatic pressure = ε₀E²/2 at surface. E = σ/ε₀ just outside. Excess pressure p = σ²/(2ε₀)
Q.198Medium
Two concentric spheres have radii r₁ (inner) and r₂ (outer). The inner sphere has charge +Q and outer sphere has charge -Q. The electric field in the region r₁ < r < r₂ is:
Answer: B
By Gauss's law, in the region between spheres, only inner charge +Q contributes. E = kQ/r², directed radially outward
Q.199Medium
A parallel plate capacitor is charged to voltage V and then isolated. If the plate separation is doubled, the energy stored becomes:
Answer: C
For isolated capacitor, charge Q remains constant. U = Q²/(2C) = Q²d/(2ε₀A). Energy is proportional to d, so doubling d doubles energy... correction: U = CV²/2, but Q is constant so U = Q²/(2C) ∝ d, energy increases
Q.200Easy
The electric flux through a closed surface enclosing a net charge of 10 μC is:
