The Particulate Nature of Matter — Free Physics HL Practice Questions

A Stirling engine operates with $n = 0.040\,\text{mol}$ of an ideal monatomic gas undergoing four processes per cycle: - $1 \to 2$: Isothermal compression at $T_c = 350\,\text{K}$, volume from $V_1 = 2.0 \times 10^{-3}\,\text{m}^3$ to $V_2 = 1.0 \times 10^{-3}\,\text{m}^3$ - $2 \to 3$: Isochoric heating from $350\,\text{K}$ to $T_h = 650\,\text{K}$ - $3 \to 4$: Isothermal expansion at $T_h = 650\,\text{K}$, volume from $1.0 \times 10^{-3}\,\text{m}^3$ to $2.0 \times 10^{-3}\,\text{m}^3$ - $4 \to 1$: Isochoric cooling from $650\,\text{K}$ to $350\,\text{K}$ Use $R = 8.31\,\text{J\,mol}^{-1}\text{K}^{-1}$ and isothermal work $W = nRT\ln\!\left(\dfrac{V_f}{V_i}\right)$.

A geothermal power plant uses steam that expands and contracts at a constant pressure of $1.2 \times 10^{6}\,\text{Pa}$. During one isobaric process, $1800\,\text{J}$ of thermal energy is transferred from the steam to the surroundings, and the volume of the steam decreases by $4.5 \times 10^{-4}\,\text{m}^3$.

An industrial heat pump operates between a cold reservoir at $T_c = 280\,\text{K}$ and a hot reservoir at $T_h = 320\,\text{K}$. The working substance is an ideal gas undergoing a cycle of three steps: - Step A→B: Isothermal compression at $280\,\text{K}$ from $V_A = 0.50\,\text{m}^3$ to $V_B = 0.20\,\text{m}^3$; heat $Q_{AB} = 1.80\,\text{kJ}$ is transferred from the gas to the cold reservoir. - Step B→C: Adiabatic compression raising the gas temperature to $320\,\text{K}$. - Step C→A: Isothermal expansion at $320\,\text{K}$ back to $V_A$; heat $Q_{CA} = 5.40\,\text{kJ}$ is delivered by the gas to the hot reservoir. $$n = 3.0\,\text{mol}, \quad R = 8.31\,\text{J mol}^{-1}\text{K}^{-1}$$

A heat engine operates between a hot reservoir at $600\,\text{K}$ and a cold reservoir at $300\,\text{K}$. In one cycle, the engine absorbs $5000\,\text{J}$ of thermal energy from the hot reservoir and rejects $3500\,\text{J}$ to the cold reservoir.

A 0.200 kg block of metal at 100 °C is placed into 0.500 kg of water at 20.0 °C in a well-insulated container. The final equilibrium temperature of the system is measured as 26.5 °C. The specific heat capacity of water is 4200 J kg$^{-1}$ K$^{-1}$.

The graph below shows the temperature of a 0.0500 kg sample of a substance as it is heated at a constant rate of 80.0 W. The sample starts as a solid and is heated until it becomes a gas. Points B and C mark the beginning and end of a horizontal plateau on the graph.

A student uses a constant-volume gas thermometer to measure the temperature of a liquid. The pressure of the gas at the triple point of water is $P_{tp} = 40.0 \ \text{kPa}$. When the thermometer is placed in the liquid, the pressure reading is $55.2 \ \text{kPa}$. The thermodynamic temperature formula is: $T = T_{tp} \times \dfrac{P}{P_{tp}}$, where $T_{tp} = 273.16 \ \text{K}$.

A 50.0 g ice cube at $-10.0\ ^\circ\text{C}$ is placed into 200 g of water at $25.0\ ^\circ\text{C}$ in a well-insulated container. Specific heat capacity of ice: $c_\text{ice} = 2100\ \text{J kg}^{-1}\text{K}^{-1}$ Specific heat capacity of water: $c_\text{w} = 4200\ \text{J kg}^{-1}\text{K}^{-1}$ Specific latent heat of fusion of ice: $L = 3.34 \times 10^5\ \text{J kg}^{-1}$

Two point charges, $q_1 = +3.0 \times 10^{-9}\,\text{C}$ and $q_2 = -5.0 \times 10^{-9}\,\text{C}$, are fixed on the $x$-axis. $q_1$ is at $x = 0$ and $q_2$ is at $x = 0.40\,\text{m}$.

A piece of silicon is doped to form an n-type semiconductor. A potential difference of $5.0\,\text{V}$ is applied across a sample of length $0.020\,\text{m}$ and cross-sectional area $4.0 \times 10^{-6}\,\text{m}^2$. The current through the sample is $0.25\,\text{A}$.

A student sets up a circuit with a battery and a single resistor. The current in the circuit is $2.0\,\text{A}$ when the potential difference across the resistor is $12\,\text{V}$. The resistor is made of a material with resistivity $\rho = 1.7 \times 10^{-8}\,\Omega\,\text{m}$, length $5.0\,\text{m}$, and circular cross-section.

An alpha particle ($q = +3.20 \times 10^{-19}\,\text{C}$, $m = 6.64 \times 10^{-27}\,\text{kg}$) is fired directly toward a stationary gold nucleus ($Q = +1.27 \times 10^{-17}\,\text{C}$, $M = 3.27 \times 10^{-25}\,\text{kg}$) from a large distance. The initial speed of the alpha particle is $v_0 = 2.0 \times 10^6\,\text{m\,s}^{-1}$. $$E_k = \tfrac{1}{2}mv^2, \quad E_p = \frac{kqQ}{r}, \quad k = 8.99 \times 10^9\,\text{N\,m}^2\,\text{C}^{-2}$$

A student places two identical balloons, one filled with $0.50 \text{ mol}$ of oxygen gas $(\text{O}_2)$ and the other with $0.25 \text{ mol}$ of nitrogen gas $(\text{N}_2)$, in a room at constant temperature and pressure.

A balloon is filled with helium gas at a temperature of $20^\circ\text{C}$ and has a volume of $2.5 \text{ m}^3$. The balloon is taken outside where the temperature drops to $-10^\circ\text{C}$. The pressure remains constant throughout.

A sealed syringe contains $20.0 \ \text{cm}^3$ of air at a pressure of $1.01 \times 10^5 \ \text{Pa}$ and temperature $20.0 \ \text{°C}$. The plunger is pushed in rapidly, compressing the gas to $10.0 \ \text{cm}^3$. During this adiabatic compression the temperature rises to $60.0 \ \text{°C}$.

A sample of carbon dioxide gas is trapped in a container at a pressure of $2.0 \times 10^5 \text{ Pa}$ and a volume of $0.40 \text{ m}^3$. The gas is compressed isothermally to a volume of $0.10 \text{ m}^3$.

A sealed flask contains neon gas at $27^\circ\text{C}$ and a pressure of $1.5 \times 10^5 \text{ Pa}$. The flask is heated until the temperature reaches $127^\circ\text{C}$. The volume of the flask remains constant throughout.

A simplified model of Earth's energy balance treats the atmosphere as a single layer that is transparent to solar radiation but absorbs all terrestrial infrared radiation. The surface emits as a blackbody at temperature $T_s$, and the atmosphere emits equally upward and downward as a blackbody at temperature $T_a$. The incoming absorbed solar radiation at the surface is $240 \text{ W m}^{-2}$.

The shows a simplified model of Earth's energy balance. Incoming solar radiation is 100 units. The atmosphere reflects 20 units to space, the surface reflects 5 units, and the atmosphere absorbs 25 units directly. The surface absorbs the remaining 50 units of solar radiation. The surface emits 110 units of terrestrial (infrared) radiation upward. The atmosphere absorbs 100 of these 110 units and re-emits 70 units back down to the surface. The remaining 10 units of terrestrial radiation pass directly to space.

The Earth's energy balance can be perturbed by changes in albedo. Increased ice melt reduces Earth's average albedo from 0.30 to 0.25. The solar constant is $S = 1360 \text{ W m}^{-2}$.

Consider a planet with no atmosphere, at a distance from the Sun where the solar constant is $S = 800 \ \text{W m}^{-2}$. Its albedo is 0.20.

A research laboratory is testing a high-temperature superconducting magnet for a medical MRI scanner. The magnet must be cooled from room temperature to its operating temperature using liquid nitrogen. Liquid nitrogen at its boiling point is introduced into a well-insulated cryostat; the nitrogen boils and the vapour is vented to the atmosphere.

A geothermal power plant in Iceland extracts heat from underground hot water and uses it to drive a steam turbine. The hot reservoir is at $T_h = 473\,\text{K}$ and the cold reservoir (atmosphere) is at $T_c = 288\,\text{K}$. The plant operator claims the actual thermal efficiency is $35\%$. Per cycle: heat input $Q_h = 5.0 \times 10^6\,\text{J}$; work output $W = 1.75 \times 10^6\,\text{J}$.