Unit 4 Comprehensive Assessment: Thermal Physics

Which of the following physical properties CANNOT be reliably utilized to construct a standard temperature scale?

A resistance thermometer has a resistance of 10.00 Ω at 0 °C (ice point) and 13.85 Ω at 100 °C (steam point). When immersed in a furnace, its resistance is measured to be 18.20 Ω. Calculate the Celsius temperature of the furnace on this linear resistance scale.

A steel bridge girder has a length of 50.0 m at 20.0 °C. If the linear expansivity of steel is 1.20 × 10⁻⁵ K⁻¹, calculate its increase in length (in millimeters) when the temperature rises to 45.0 °C on a hot sunny day.

A brass rod and an iron rod have lengths L₁ and L₂ at 0 °C. The difference between their lengths (L₂ - L₁) remains strictly constant at all temperatures. If the linear expansivity of brass is α_b = 1.9 × 10⁻⁵ K⁻¹ and that of iron is α_i = 1.2 × 10⁻⁵ K⁻¹, calculate the ratio L₁ / L₂ at 0 °C.

Calculate the quantity of heat energy (in kilojoules) required to heat 2.50 kg of water from 25.0 °C to 85.0 °C. (Specific heat capacity of water c_w = 4186 J kg⁻¹ K⁻¹).

A 0.400 kg block of aluminium at 100.0 °C is dropped into a copper calorimeter of mass 0.150 kg containing 0.300 kg of water at 20.0 °C. Neglecting heat losses, calculate the final equilibrium temperature in °C. (c_water = 4186 J kg⁻¹ K⁻¹, c_copper = 385 J kg⁻¹ K⁻¹, c_aluminium = 900 J kg⁻¹ K⁻¹).

A trapped mass of dry air occupies a volume of 250 cm³ under a pressure of 1.00 × 10⁵ Pa. If the gas is compressed isothermally until its volume decreases to 100 cm³, calculate the new pressure of the gas in kPa.

An air bubble of volume 2.00 cm³ forms at the bottom of a deep lake where the water depth is 30.0 m and water temperature is 7.0 °C. It rises to the surface where the temperature is 27.0 °C and atmospheric pressure is 1.00 × 10⁵ Pa. Calculate the volume of the bubble (in cm³) just before it breaks the surface. (Density of water = 1000 kg m⁻³, g = 9.8 m s⁻²).

A copper bar has a cross-sectional area of 1.20 × 10⁻³ m² and a length of 0.50 m. One end is maintained in steam at 100.0 °C and the other end in melting ice at 0.0 °C. Assuming steady-state conduction and no side heat losses, calculate the rate of heat conduction (in Watts) along the bar. (Thermal conductivity of copper k = 390 W m⁻¹ K⁻¹).

In an isobaric expansion at a constant pressure of 2.00 × 10⁵ Pa, a gas expands in volume from 0.010 m³ to 0.035 m³. During this process, 8500 J of heat is supplied to the gas. Calculate the increase in internal energy ΔU (in Joules) of the gas.

A student uses a uniform capillary Quill tube of uniform internal bore to investigate Boyle’s law. A column of dry air is trapped at the closed end by a mercury index pellet of length h = 15.0 cm. Atmospheric pressure during the experiment is H = 75.0 cmHg.

In an experiment to investigate Charles’s law and estimate absolute zero, a sample of dry air trapped in a uniform capillary tube is heated in a water bath. The length l of the air column is recorded at various temperatures θ, producing a linear graph with equation l = 0.080 θ + 21.84 where l is in cm and θ is in °C.

A fixed volume of gas inside a constant-volume gas thermometer has a pressure of P₀ = 1.00 × 10⁵ Pa at the ice point (0.0 °C / 273.15 K). Calculate the pressure of the gas in pascals (Pa) at the steam point (100.0 °C / 373.15 K). Give your answer to the nearest whole number.

A sealed rigid container of volume V = 0.025 m³ contains N = 6.02 × 10²³ molecules of helium gas (monatomic, molar mass M_mol = 4.00 × 10⁻³ kg mol⁻¹) at temperature T = 300 K. The Boltzmann constant is k_B = 1.38 × 10⁻²³ J K⁻¹ and Avogadro constant is N_A = 6.02 × 10²³ mol⁻¹.

According to the kinetic theory of ideal gases, the pressure P exerted by a gas of density ρ and root-mean-square speed c_rms is given by:

The root-mean-square speed of nitrogen molecules at temperature T₁ = 300 K is 517 m s⁻¹. At what temperature T₂ (in kelvin, K) will the root-mean-square speed be doubled to 1034 m s⁻¹?

One mole of an ideal monatomic gas (C_v = 1.5 R, C_p = 2.5 R, where R = 8.31 J mol⁻¹ K⁻¹) is initially at pressure P₁ = 1.00 × 10⁵ Pa and temperature T₁ = 300 K. The gas undergoes an isobaric expansion (constant pressure) until its temperature reaches T₂ = 450 K.

During a reversible adiabatic expansion of an ideal gas:

A cylindrical brass rod of thermal conductivity k = 110 W m⁻¹ K⁻¹, length L = 0.500 m, and circular cross-sectional radius r = 0.020 m is perfectly lagged along its cylindrical sides to prevent radial heat loss. One end is maintained at steady temperature θ₁ = 100.0 °C by steam, and the other end is kept at θ₂ = 20.0 °C in melting ice.

According to Stefan-Boltzmann’s law, the total radiant energy emitted per second per unit surface area of a black body is directly proportional to: