Heat & Thermodynamics: 29 MCQs with Explanations

Efficiency η = 1 - T_c/T_h = 1 - 300/400 = 1 - 0.75 = 0.25 or 25%.

For adiabatic process (no heat exchange), PV^γ = constant, where γ = Cp/Cv.

For diatomic gas: C_v = 5R/2, C_p = 7R/2, so γ = C_p/C_v = 7/5 = 1.40.

For ideal gas, internal energy depends only on temperature. In isothermal process, ΔT = 0, so ΔU = 0.

Stefan-Boltzmann law: P ∝ T⁴. If T doubles, P increases by 2⁴ = 16 times.

Second law (Kelvin-Planck statement) states that no heat engine can convert all heat into work in a cyclic process.

η = 1 - T_c/T_h = 1 - 300/500 = 1 - 0.6 = 0.4 or 40%.

Efficiency η = 1 - T₂/T₁ = (T₁-T₂)/T₁, where T₁ is source temperature and T₂ is sink temperature (in kelvin).

From kinetic theory: vᵣₘₛ = √(3RT/M), so vᵣₘₛ ∝ √T, where T is absolute temperature and M is molar mass.

For diatomic gases (at room temperature): degrees of freedom f = 5 (3 translational + 2 rotational). γ = 1 + 2/f = 1 + 2/5 = 7/5 = 1.4.

Specific heat capacity of water = 1 cal/g°C = 1 kcal/kg°C = 4186 J/kg°C ≈ 4200 J/kg°C. So 1 kg water requires 1 kilocalorie (or 4200 J) to raise temperature by 1°C.

Efficiency η = 1 - T₂/T₁. For η = 1, either T₂ = 0 K (impossible per third law of thermodynamics) or T₁ = ∞ (impossible). Also, Kelvin-Planck statement of second law forbids 100% conversion of heat to work in cyclic process.

For monoatomic gases: Cp = 5R/2, Cv = 3R/2, so γ = Cp/Cv = 5/3 ≈ 1.67.

Q = mL = 1 × 336,000 = 336,000 J = 336 kJ.

Efficiency η = 1 - T_c/T_h = 1 - 300/500 = 1 - 0.6 = 0.4 or 40%.

For monatomic gas: C_v = 3R/2, C_p = 5R/2, so γ = C_p/C_v = 5/3 ≈ 1.67.

Radioactivity (discovered by Becquerel, 1896) is spontaneous emission of α, β, or γ radiation by unstable nuclei.

CO₂ and H₂O vapor absorb infrared radiation emitted by Earth's surface, trapping heat in atmosphere.

Ozone (O₃) in stratosphere absorbs harmful UV-B and UV-C radiation (200-310 nm), protecting life on Earth.

'Isothermal' means 'at constant temperature'. In an isothermal process, the temperature of the system remains constant throughout. For an ideal gas, this implies that internal energy (ΔU = 0) does not change.

A heat engine is a device that takes in heat from a hot reservoir, converts part of it into useful work (like moving a piston), and rejects the remaining waste heat to a cold reservoir.

To find where °C = °F, use the conversion formula: F = (9/5)C + 32. Substitute F = C: C = (9/5)C + 32. Solving gives C - (9/5)C = 32 => (-4/5)C = 32 => C = -40°. So, -40°C = -40°F.

An adiabatic process is one in which no heat is exchanged between the system and its surroundings (Q = 0). This does not mean temperature is constant (that's isothermal). The total heat content is not a defined state function.

Carnot's theorem states that the efficiency of a Carnot engine (the most efficient heat engine) depends solely on the absolute temperatures of the hot reservoir (T₁) and the cold reservoir (T₂): η = 1 - T₂/T₁.

The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero temperature is exactly zero. At 0 K, there is only one possible microstate (perfect order), so entropy S = k ln W = k ln 1 = 0.

The ideal gas law (PV = nRT) combines Boyle's law (P ∝ 1/V), Charles's law (V ∝ T), and Avogadro's law (V ∝ n) into a single equation of state for an ideal gas.

According to Stefan-Boltzmann law, the total energy radiated per second per unit area (E) is proportional to the fourth power of its absolute temperature: E = σT⁴. If T becomes 2T, then E becomes (2)⁴ = 16 times.

The moderator (like graphite or heavy water) slows down the fast neutrons produced in fission to thermal neutrons. Thermal neutrons are more effective at causing further fission in U-235.

Specific heat capacity is defined as the amount of heat energy required to raise the temperature of a unit mass (1 kg) of a substance by one degree kelvin (or one degree Celsius).