This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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You're on a roll — Problem 1: Calorimetry Experiment Step 1: Identify the given values for the metal and water. For the metal: Mass, m_m = 0.05 kg Initial temperature, T_m,i = 200.0 °C Final equilibrium temperature, T_f = 22.4 °C Change in temperature, T_m = T_f - T_m,i = 22.4 °C - 200.0 °C = -177.6 °C Specific heat capacity, c_m = ? For the water: Mass, m_w = 0.40 kg Initial temperature, T_w,i = 20.0 °C Final equilibrium temperature, T_f = 22.4 °C Change in temperature, T_w = T_f - T_w,i = 22.4 °C - 20.0 °C = 2.4 °C Specific heat capacity, c_w = 4.186 kJ/(kg·°C) = 4186 J/(kg·°C) Step 2: Apply the principle of calorimetry: Heat lost by metal = Heat gained by water. |Q_m| = Q_w m_m c_m | T_m| = m_w c_w T_w Step 3: Calculate the heat gained by the water. Q_w = (0.40 kg) × (4186 J/(kg·°C)) × (2.4 °C) Q_w = 4018.56 J Step 4: Substitute the values into the calorimetry equation and solve for c_m. (0.05 kg) × c_m × |-177.6 °C| = 4018.56 J (0.05 kg) × c_m × (177.6 °C) = 4018.56 J c_m = 4018.56 J(0.05 kg) × (177.6 °C) c_m = 4018.56 J8.88 kg·°C c_m ≈ 452.54 J/(kg·°C) Step 5: Select the closest option. The calculated value 452.54 J/(kg·°C) is closest to 453 J/(kg·°C). The specific heat capacity of the metal is 453 J/(kg·°C). --- Problem 2: Adiabatic Free Expansion Step 1: Understand the definitions of an adiabatic process and free expansion. An adiabatic process is one where no heat is exchanged with the surroundings, so Q = 0. A free expansion occurs when a gas expands into a vacuum. In this process, there is no external pressure for the gas to work against. Step 2: Calculate the work done. The work done by a gas is given by W = P_ext dV, where P_ext is the external pressure. For a free expansion, the external pressure P_ext = 0. Therefore, the work done by the gas is: W = 0 × V W = 0 J The information about the temperature decrease is a characteristic of a real gas undergoing free expansion, or a non-ideal adiabatic process. However, for an ideal gas undergoing a free expansion, the work done is defined as zero because there is no external pressure. The work done by the gas in the process is 0 J. What's next?