Category: HC Verma Part 2: Heat & Thermo

Problem Statement A solid sphere of radius 5 cm, mass 1 kg, specific heat 500 J/kg·K, emissivity 0.9 is at 500 K in a surrounding at 300 K. Find its initial rate of cooling. ($\sigma = 5.67 \times 10^{-8}$ W/m²·K⁴) Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem…

Problem Statement Solve the thermodynamics problem: Solve the thermodynamics problem: A flat plate of area 0.5 m² at 60°C loses heat by convection to air at 20°C. The convective heat transfer coefficient is $h = 25$ W/m²·K. Find the rate of heat loss. $A = 0.5$ m² $T_{surface} = 60°C$, $T_{air} = 20°C$, $\Delta T…

Problem Statement Solve the thermodynamics problem: A steam pipe (inner radius $r_1 = 5$ cm, outer radius $r_2 = 7$ cm, $k = 50$ W/m·K) carries steam at 200°C. The outer surface is at 50°C. Find the rate of heat loss per metre length. All quantities, constants, and constraints stated in the problem above Physical…

Problem Statement Solve the thermodynamics problem: Mars is 1.52 AU from the Sun (Earth is 1 AU). If Earth’s effective temperature is 280 K, find Mars’s effective temperature. (Assume both planets are perfect black bodies.) All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Given Information…

Problem Statement Solve the thermodynamics problem: Solve the thermodynamics problem: A uniform rod of length $L$ and thermal conductivity $k$ has one end at $T_1$ and the other at $T_2$. Find the temperature at the midpoint and the heat current through the rod. Rod length $L$, conductivity $k$, area $A$ Ends at $T_1$ and $T_2$…

Problem Statement Analyze the circuit: Analyze the circuit: A body at 727°C emits 60% of the radiation of a perfect black body at the same temperature. Find (a) its emissivity, (b) its absorptivity for radiation from a source at 727°C. ($\sigma = 5.67 \times 10^{-8}$ W/m²·K⁴, $A = 0.5$ m²) $T = 727°C = 1000$…

Problem Statement Solve the thermodynamics problem: The solar constant is 1.4 kW/m². Assuming Earth is a perfect black body in radiative equilibrium with the Sun, estimate Earth’s mean surface temperature. (Earth’s radius $R_E = 6.4 \times 10^6$ m, $\sigma = 5.67 \times 10^{-8}$ W/m²·K⁴) All quantities, constants, and constraints stated in the proble Given Information…

Problem Statement A wall consists of 10 cm of concrete ($k_1 = 0.8$ W/m·K) and 5 cm of insulating board ($k_2 = 0.05$ W/m·K). The inner surface is at 25°C and the outer is at -5°C. Find the temperature at the interface and the heat flux. ($A = 1$ m²) Given Information See problem statement…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: A body of emissivity $\epsilon = 0.8$ and surface area $A = 0.2$ m² is at 400 K in a room at 300 K. Find the net rate of heat loss by radiation. ($\sigma = 5.67 \times 10^{-8}$ W/m²·K⁴) $\epsilon = 0.8$, $A = 0.2$…

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: Find the wavelength at which radiation emitted by the Sun is maximum, given the Sun’s surface temperature is 5778 K. Also find the peak wavelength for a body at 300 K (room temperature). ($b = 2.898 \times 10^{-3}$ m·K) Wien’s constant $b = 2.898 \times…