After a free expansion to increase its volume by a factor of seven, a mole of ideal monatomic gas is compressed back to its original volume isobarically and then warmed up isochorically to its original temperature. What is the heat added to the gas in the final step to restoring its original state? (Use the following as necessary: Po for the initial pressure and Vo for the initial volume.)
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- Part A: 10 moles of ideal gas initially at 10 atm and 250 K is expanded isothermally and reversibly to a final pressure of 2 atm. Calculate W, AU, and Q in Joules. Part B: The same gas in problem A, starting in the same initial state, is expanded isothermally against a constant external pressure of 2 atm, to a final pressure of 2 atm. Calculate W, AU, and Q in Joules for this irreversible process. Part C: The same gas in part B, starting in the same initial state, is expanded isothermally to a final pressure of 2 atm. The process is carried out in 4 stages. First the gas is expanded against a constant pressure of 8 atm, to 8 atm. Then the gas is expanded against a constant pressure of 6 atm, to 6 atm. Then the gas is expanded against a constant pressure of 4 atm, to 4 atm. Finally, the gas is expanded against a constant pressure of 2 atm, to 2 atm. Calculate W, AU, and Q in Joules for the 4-step process.When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV to the power of 1.4 = C where C is a constant. Suppose that at a certain instant the volume is 480 cubic centimeters and the pressure is 75 kPa and is decreasing at a rate of 10 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant? Please Write legibleAn insulated container contains two moles of an ideal gas at atmospheric pressure. Keeping the pressure constant, if the temperature of the gas is increased by 50 °C, then its volume increases by 400 cm3 and if the temperature is increased by 100 °C, then its volume increases by 600 cm³. Determine the initial volume and temperature of the gas. (Write the equation of ideal gas initially, after the temperature increase of 50 °C, and after increase of temperature by 100 °C. Combine these three equations to find the initial volume and temperature)
- A container is filled with an ideal diatomic gas to a pressure and volume of P1 and V1, respectively. The gas is then warmed in a two-step process that increases the pressure by a factor of five and the volume by a factor of four. Determine the amount of energy transferred to the gas by heat if the first step is carried out at constant volume and the second step at constant pressure. (Use any variable or symbol stated above as necessary.)Problem 4: Consider a cylinder with a movable piston containing n moles of an ideal gas. The entire apparatus is immersed in a constant temperature bath of temperature T Kelvin. The piston pushes slowly outward on an external body which matches the force momentarily at each instant so that the gas expands quasi-statically from a volume V1 to V2 at constant temperature T. The isothermal process is shown in the figure above, where the pressure p is related to the volume V by the ideal gas law as follows: pV = nRT, where R is the gas constant. Part (b) For n = 3 moles, T = 350 K, and V2 = 2.5V1, determine the work done by the gas on the external body. The gas constant is R = 8.314 J K-1 mol-1.A good explanation would be really helpful
- A particular thermodynamic cycle acting on a monatomic ideal gas (y = 1.67) includes an isobaric expansion, an isochoric cooling, and then a isothermic contraction. The PV diagram is shown in the image below. P V The isobaric expansion occurs at a pressure of 2.265 × 105 Pa and changes the volume of the gas from 5.9 × 10 2 m³ to 10.98 × 10-2 m³. What is the efficiency of the process?You would like to raise the temperature of an ideal gas from 295 K to 960 K in an adiabatic process. a)What compression ratio will do the job for a monatomic gas? b)What compression ratio will do the job for a diatomic gas?1.7 Ideal gas response functions Find the thermal expansion coefficient and the isothermal compressibility for an ideal gas and show that in this case Cp - Cy = - a² can be reduced to Cp – Cy = Nkg for the molar specific heats. TV Кт
- A flexible box contains 5.60 grams of nitrogen gas (N2) which is maintained at a constant pressure of 1.35 x 10$ Pa. The box is placed over a fire, causing the volume to increase from 0.00200 m3 to 0.00300 m³. Find the increase in temperature of the gas. (For N2 molar mass M = 28 grams.)Part A: If you supply 2950 J of heat to 6.00 moles of an ideal diatomic gas initially at 23.0 ∘C in a perfectly rigid container, what will be the final temperature of the gas? Express in degrees Celsius. Part B: Suppose the gas in the container were an ideal monatomic gas instead. How much heat would you need to add to produce the same temperature change? Part C: Which pV diagram expresses these processes?