Вопрос
3. A 60 liter vessel is filled with oxygen at 125 bar Determine the final pressure of oxygen and the amount of heat supplied, if the initial temperature of oxygen is 10^circ C and the final tem- perature is 30^circ C Consider the heat capacity of oxygen as constant.
Решения
4.2
(294 Голоса)
Ольга
мастер · Репетитор 5 лет
Ответ
To solve this problem, we can use the ideal gas law and the first law of thermodynamics.Given information:- Volume of the vessel: 60 liters- Initial pressure of oxygen: 125 bar- Initial temperature of oxygen: 10°C- Final temperature of oxygen: 30°C- Heat capacity of oxygen is constantStep 1: Convert the given temperatures to Kelvin.Initial temperature (T1) = 10°C + 273.15 = 283.15 KFinal temperature (T2) = 30°C + 273.15 = 303.15 KStep 2: Use the ideal gas law to find the final pressure of oxygen.The ideal gas law is given by the equation:PV = nRTWhere:P = PressureV = Volumen = Number of molesR = Universal gas constantT = TemperatureRearranging the equation, we get:P = nRT / VSince the volume of the vessel is constant, the number of moles of oxygen remains the same. Therefore, we can write:P1V1 = P2V2Substituting the given values, we get:125 bar × 60 L = P260 LSolving for P2, we get:P2 = 125 barTherefore, the final pressure of oxygen is 125 bar.Step 3: Calculate the amount of heat supplied.The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.The change in internal energy (ΔU) can be calculated using the formula:ΔU = nCpΔTWhere:n = Number of molesCp = Molar heat capacity at constant pressureΔT = Change in temperatureSince the heat capacity of oxygen is constant, we can write:ΔU = nCp(T2 - T1)Substituting the given values, we get:ΔU = nCp(303.15 K - 283.15 K)Simplifying, we get:ΔU = nCp(20 K)Therefore, the amount of heat supplied is nCp(20 K), where n is the number of moles of oxygen.