Category: HC Verma Part 2: Heat & Thermo

Problem Statement Solve the thermodynamics problem: 10 g of steam at 100°C is passed into 100 g of water at 20°C. Find the final temperature. ($L_{steam} = 2.26 \times 10^6$ J/kg, $c_w = 4200$ J/kg·K) $m_{steam} = 10$ g = 0.01 kg at 100°C $m_w = 100$ g = 0.1 kg at 20°C Steam first…

Problem Statement Solve the thermodynamics problem: A 50-g copper calorimeter contains 200 g of water at 20°C. A 100-g metal block at 100°C is dropped into it. The final temperature is 25°C. Find the specific heat of the metal. ($c_{Cu} = 390$ J/kg·K, $c_w = 4200$ J/kg·K) $m_{metal} = 100$ g = 0.1 kg, $T_{metal}…

Problem Statement Solve the nuclear physics problem: 100 g of ice at 0°C is added to 200 g of water at 40°C in a calorimeter. Find the final temperature. ($L_{ice} = 336000$ J/kg, $c_w = 4200$ J/kg·K, water equivalent of calorimeter = 10 g) $m_{ice} = 100$ g = 0.1 kg, $T_{ice} = 0°C$ $m_w…

Problem Statement Solve the thermodynamics problem: 200 g of water at 80°C is mixed with 300 g of water at 20°C. Find the equilibrium temperature. (Neglect heat losses.) $m_1 = 200$ g, $T_1 = 80°C$ (hot water) $m_2 = 300$ g, $T_2 = 20°C$ (cold water) $c = 4200$ J/kg·K (same for both) Principle of…

Problem Statement Solve the thermodynamics problem: How much heat is required to raise the temperature of 500 g of water from 20°C to 100°C? (Specific heat of water $c = 4200$ J/kg·K) $m = 500$ g $= 0.5$ kg $\Delta T = 100 – 20 = 80°C$ $c = 4200$ J/kg·K The heat required to…

Problem Statement Solve the fluid mechanics problem: One mole of an ideal monatomic gas is heated at constant volume from 0°C to 100°C. Find the increase in internal energy. ($R = 8.314$ J/mol·K) $n = 1$ mol (monatomic, $f = 3$) $\Delta T = 100°C = 100$ K Constant volume Internal energy of an ideal…

Problem Statement Solve the thermodynamics problem: At what temperature will the rms speed of oxygen molecules equal 500 m/s? ($M_{O_2} = 32 \times 10^{-3}$ kg/mol, $R = 8.314$ J/mol·K) $v_{rms} = 500$ m/s $M = 32 \times 10^{-3}$ kg/mol $$v_{rms} = \sqrt{\frac{3RT}{M}} \Rightarrow T = \frac{Mv_{rms}^2}{3R}$$ Step 1: Square the rms speed equation. $$v Given…

Problem Statement Solve the momentum/collision problem: Estimate the average number of collisions per second for a nitrogen molecule at 300 K and 1 atm. ($d = 3.7 \times 10^{-10}$ m, $M = 28 \times 10^{-3}$ kg/mol) $d = 3.7 \times 10^{-10}$ m $T = 300$ K, $P = 1.013 \times 10^5$ Pa $M = 28…

Problem Statement Given $R = 8.314$ J/mol·K and $N_A = 6.022 \times 10^{23}$ mol$^{-1}$, calculate Boltzmann’s constant $k_B$. Also find the average kinetic energy of a gas molecule at 27°C. 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 Statement Solve the fluid mechanics problem: A vessel contains 2 mol of H₂ and 3 mol of N₂ at 300 K. The volume of the vessel is 10 L. Find the total pressure and the partial pressure of each gas. ($R = 8.314$ J/mol·K) $n_{H_2} = 2$ mol, $n_{N_2} = 3$ mol $T =…