Category: HC Verma Part 2: Heat & Thermo

Problem Statement Solve the elasticity problem: A 1-m long steel wire of cross-section $1 \text{ mm}^2$ is stretched by 1 mm at 30°C. Find the temperature at which the wire becomes tension-free. ($\alpha = 1.2 \times 10^{-5}$ °C$^{-1}$, $Y = 2 \times 10^{11}$ Pa) $L = 1$ m, $A = 1 \text{ mm}^2 = 10^{-6}$…

Problem Statement Solve the fluid mechanics problem: A steel cylinder contains gas at pressure $10^5$ Pa at 27°C. The cylinder is heated to 127°C. Find the new pressure, assuming the cylinder volume doesn’t change. $P_1 = 10^5$ Pa, $T_1 = 27°C = 300$ K $T_2 = 127°C = 400$ K Volume constant (rigid cylinder) At…

Problem Statement Solve the thermodynamics problem: A steel rod and an aluminium rod have the same length at 40°C. At what temperature is the steel rod 0.01% longer than the aluminium rod? ($\alpha_{steel} = 1.2 \times 10^{-5}$, $\alpha_{Al} = 2.3 \times 10^{-5}$ °C$^{-1}$) $L_{steel} = L_{Al} = L$ at 40°C Required: steel is 0.01% longer,…

Problem Statement The density of mercury at 0°C is $13600$ kg/m³. Find its density at 100°C. ($\gamma_{Hg} = 1.8 \times 10^{-4}$ °C$^{-1}$) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key…

Problem Statement A brass ring has inner diameter 10.00 cm at 30°C. A steel rod has diameter 10.01 cm at 30°C. To what temperature must the ring be heated so that it just fits over the rod? ($\alpha_{brass} = 2.0 \times 10^{-5}$ °C$^{-1}$) Given Information All quantities, constants, and constraints stated in the problem above…

Problem Statement Steel railway tracks each 12.0 m long are laid at 20°C. What gap should be left between consecutive tracks so that there is no compression when temperature reaches 50°C? ($\alpha = 1.2 \times 10^{-5}$ °C$^{-1}$) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see…

Problem Statement Solve the thermodynamics problem: In a constant-volume gas thermometer, the pressure at the triple point of water is $1.5 \times 10^4$ Pa. What is the temperature when the pressure is $2.0 \times 10^4$ Pa? $P_{tr} = 1.5 \times 10^4$ Pa at $T_{tr} = 273.16$ K $P = 2.0 \times 10^4$ Pa at unknown…

Problem Statement Solve the thermodynamics problem: The triple point of water is assigned the value 273.16 K in the Kelvin scale. Explain why the triple point is chosen rather than the ice point (0°C) as the reference. Triple point temperature: $T_{tr} = 273.16$ K Ice point: 273.15 K (at 1 atm pressure) A thermometric fixed…

Problem Statement Analyze the circuit: The resistance of a platinum wire at 0°C is 5 Ω and at 100°C is 5.39 Ω. If the resistance at an unknown temperature is 5.19 Ω, find that temperature. (Assume linear variation.) $R_0 = 5.00$ Ω at 0°C $R_{100} = 5.39$ Ω at 100°C $R_T = 5.19$ Ω at…

Problem Statement Solve the thermodynamics problem: A brass rod and a steel rod have lengths 1.0 m and 2.0 m respectively at 0°C. Find the temperature at which their difference in length is 0.002 m more than at 0°C. ($\alpha_{brass} = 2.0 \times 10^{-5}$, $\alpha_{steel} = 1.2 \times 10^{-5}$ °C$^{-1}$) $L_b = 1.0$ m (brass),…