Category: HC Verma Part 2: Heat & Thermo

Problem Statement Solve the thermodynamics problem: At constant pressure, 2 mol of a diatomic ideal gas absorbs 2495 J of heat and its temperature rises by 30 K. Find $C_P$. ($R = 8.314$ J/mol·K) $n = 2$ mol, $Q = 2495$ J at constant pressure $\Delta T = 30$ K At constant pressure: $$Q =…

Problem Statement Solve the thermodynamics problem: Calculate the heat required to convert 200 g of water at 25°C completely to steam at 100°C. ($c_w = 4.2$ J/g·K, $L_{vap} = 2260$ J/g) $m = 200$ g $T_i = 25°C$, $T_f = 100°C$ (as steam) Two-stage process: Heat water from 25°C to 100°C: $Q_1 = mc_w(100-25)$ Vaporize…

Problem Statement Solve the thermodynamics problem: What is the minimum mass of ice at 0°C needed to cool 300 g of water from 30°C to 10°C? ($L_{ice} = 336$ J/g, $c_w = 4.2$ J/g·K) $m_w = 300$ g, $T_i = 30°C$, $T_f = 10°C$ $\Delta T_w = 20°C$ Heat given by water = Heat absorbed…

Problem Statement Solve the thermodynamics problem: 500 g of ice at 0°C is added to 300 g of water at 50°C. Find the final state and temperature. ($L_{ice} = 336$ J/g, $c_w = 4.2$ J/g·K) $m_{ice} = 500$ g at 0°C $m_w = 300$ g at 50°C Compare heat available vs heat needed to melt…

Problem Statement Solve the thermodynamics problem: A burner releases heat at 2000 J/s. How long will it take to heat 10 kg of water from 25°C to 95°C? (Assume 80% efficiency, $c_w = 4200$ J/kg·K) Power output: $P = 2000$ J/s Efficiency $\eta = 80\% = 0.8$ $m_w = 10$ kg, $\Delta T = 70°C$…

Problem Statement Solve the thermodynamics problem: In Joule’s paddle wheel experiment, a weight of 5 kg falls through 3 m and heats 500 g of water. Find the rise in temperature of the water. ($J = 4.2$ J/cal, $c_w = 1$ cal/g·°C, $g = 9.8$ m/s²) $m_{weight} = 5$ kg, $h = 3$ m $m_w…

Problem Statement Solve the thermodynamics problem: A human body loses heat through perspiration at the rate of 600 kcal/hr. If all of this is from evaporation of sweat, how much sweat is evaporated per hour? ($L_{evap} = 2450$ kJ/kg, $1$ kcal $= 4186$ J) Heat loss rate: $600$ kcal/hr $L_{evap} = 2450$ kJ/kg Heat removed…

Problem Statement Solve the thermodynamics problem: Find the heat required to convert 500 g of ice at -10°C to water at 20°C. ($c_{ice} = 2100$ J/kg·K, $L_{ice} = 336000$ J/kg, $c_w = 4200$ J/kg·K) $m = 500$ g = 0.5 kg Initial: ice at $-10°C$; Final: water at $20°C$ The process has three distinct stages,…

Problem Statement Solve the thermodynamics problem: Equal masses of ice at 0°C and steam at 100°C are mixed. Find the final state and temperature. ($L_{ice} = 336$ J/g, $L_{steam} = 2260$ J/g, $c_w = 4.2$ J/g·K) $m_{ice} = m_{steam} = m$ $T_{ice} = 0°C$, $T_{steam} = 100°C$ Heat released by steam condensing + cooling: $Q_{released}…

Problem Statement Solve the thermodynamics problem: A calorimeter of mass 50 g and specific heat 400 J/kg·K contains 200 g of water at 25°C. What is the water equivalent of the calorimeter? What is the effective thermal capacity of the system? $m_{cal} = 50$ g = 0.05 kg, $c_{cal} = 400$ J/kg·K $m_w = 200$…