Consider an ideal gas containing N atoms in a container of volume Pressure P, and absolute temperature T1 (not to be confused with K. E. T). Use the virtual theorem to derive the equation of state for a perfect gas.
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Consider an ideal gas containing N atoms in a container of volume Pressure P, and
absolute temperature T1 (not to be confused with K. E. T). Use the virtual theorem to
derive the equation of state for a perfect gas.
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- Help please answer this calculus Question: The pressure P and volume V of an expanding gas are related by the formula PV^b =c, where b and C are constants (this holds in adiabatic expansion, with or without loss). Find the dP/dt if b=1.6, P=10 kPa, V=60 cm^3, and dV/dt =80 cm^3/min. (Use symbolic notation and fractions where needed).人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT 1. An ideal gas undergoes the changes shown in the PV plane. a) Establish for each pair of variables the corresponding sign (>,=,<) b) Establish the corresponding values of the polytropic exponent k (0, 1, 1, ∞) P 3 Isotherm 1-2 2-3 3-4 4-1 P1 P2 V1 |V2 P2 P3 V2 V3 海鮮 P3 P4 V3 V4 P4 P1 V4 V1 Process Isotherm T1 T2 T3 T4 T2 T3 T4 T₁ kConsider phase transitions in conditions of variable pressure, volume and temperature. In the phase diagram for a single component system, the critical point defines the pressure, Pc, and temperature, Tc, at the end of the liquid-vapour co-existence line in P-T coordinates. A system consists of one mole of van der Waals gas, whose equation of state is P+ (V - b) = RT , where R is the universal gas constant. Using the information from (a) (ii), show that, for such a system, the molar volume at the critical point is given by V. = 3b. Show also that the other two parameters at the critical point are 8a and Pc Tc 27 Rb a 27b2
- The P-V diagram relates to a fixed quantity of O2, assumed to be an ideal gas. The temperature at point C is 140oC. What is the total mass of O2?Show ALL pertinent solutions. Tabulate data of iteration after the solution.Suppose you have 0.53 moles of an ideal gas. What is the average kinetic energy of that gas (in units of kJ) if the temperature of the gas is 280.2K? Note: It is understood that the unit of your answer is some number of kilo-Joules, however do not explicitly include units in your answer. Enter only a number. If you do enter a unit ("kJ" in this case), you answer will be counted wrong.
- Show that for an ideal gas (@T/ƏV)u = 0, and (@T/ƏP)H= 0.Derive the thermodynamic equation of state from the fundamental equation for enthalpy (OT), ән (OH!) T =V-T HINT: you will need to use a Maxwell relation. Derive an expression for an ideal and (b) a van der Waals gas. ән Әр T for (a)Consider a planetary atmosphere consisting of an ideal gas of atoms, each of mass m. The temperature T is regarded to be constant, independent of the height z above ground level. The acceleration of gravity g is constant, and the pressure at ground level is Po. Find the pressure as a function of z. (Hint: consider a thin slab of the atmosphere, and write and solve a simple differential equation.)
- A container encloses 2 mol of an ideal gas that has molar mass M₁ and 0.5 mol of a second ideal gas that has molar mass M2 = 3M₁. What fraction of the total pressure on the container wall is attributable to the second gas? Note: The kinetic theory explanation of pressure leads to the experimentally discovered law of partial pressures for a mixture of gases that do not react chemically: The total pressure exerted by the mixture is equal to the sum of the pressures that the several gases would exert separately if each were to occupy the vessel alone.Consider an ideal gas of N molecules, in equilibrium in a container of volume V . Calculatea. the probability p1 of finding all molecules concentrated in a volume V /3 (macrostate 1);b. the probability p2 of finding all molecules concentrated in a volume 2V /3 (macrostate 2);c. the probability p of finding N/3 of the molecules concentrated in a volume V / 3 and the othersin the remaining volume;d. the entropy difference ∆S = S2 - S1 between states 1 and 2;e. the numerical values of p1, p2, and p for N = 9.The image shows the example of finding the number of vacancies in 1 cubic meter of copper (Cu) at 1000 degrees celcius (1273 k) considering the image data. Replicating the problem in the image, calculate the number of vacancies but at room temperature.Explain why there is such a difference in the number of vacancies at both temperatures.