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A 4.00 L sample of a diatomic ideal gas with specific heat ratio 1.40, confined to a cylinder, is carried through a closed cycle. The gas is initially at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume.
(d) Find the temperature at the end of the cycle.
K
(e) What was the net work done on the gas for this cycle?
J
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- As a 3.00-mol sample of a monatomic ideal gas expands adiabatically, the work done on it is −2.50 103 J. The initial temperature and pressure of the gas are 400 K and 2.60 atm. Calculate the following. (a) the final temperature K(b) the final pressure atmA 3-mole of a monatomic ideal gas undergoes an isothermal expansion at 450 K, as the volume increased from 0.010 m³ to 0.060 m³. What is the work done by the gas and the change in the internal energy of the gas respectively during this process? (R = 8.31 J/mol · K)In a constant-volume process, 208 J of energy is transferred by heat to 1.07 mol of an ideal monatomic gas initially at 303 K. (a) Find the work done on the gas. (b) Find the increase in internal energy of the gas. (c) Find its final temperature. K
- A 2.00 mol sample of an ideal diatomic gas at a pressure of 1.10 atm and temperature of 420 K undergoes a process in which its pressure increases linearly with temperature. The final temperature and pressure are 720 K and 1.70 atm . Fid the change in internal energy, work done by the gas, and heat added.A 1 mol sample of a diatomic ideal gas (γ=1.4) expands slowly and adiabatically from a pressure of 18 atm and a volume of 3 L to a final volume of 18 L. What is the final temprature (in K) of the gas? ( Answer no decimal )A monatomic ideal gas initially fills a V0 = 0.45 m3 container at P0 = 85 kPa. The gas undergoes an isobaric expansion to V1 = 1.4 m3. Next it undergoes an isovolumetric cooling to its initial temperature T0. Finally it undergoes an isothermal compression to its initial pressure and volume. 1 Calculate the work done by the gas, W1, in kilojoules, during the isobaric expansion (first process). 2 Calculate the heat absorbed Q1, in kilojoules, during the isobaric expansion (first process). 3 Write an expression for the change in internal energy, ΔU1 during the isobaric expansion (first process). 4 Calculate the work done by the gas, W2, in kilojoules, during the isovolumetric cooling (second process). 5 Calculate the heat absorbed Q2, in kilojoules, during the isovolumetric cooling (second process). 6 Calculate the change in internal energy by the gas, ΔU2, in kilojoules, during the isovolumetric cooling (second process). 7 Calculate the work done by the gas, W3, in kilojoules,…
- In an engine, 0.25 mol of an ideal monatomic gas in the cylinder expands rapidly and adiabatically against the piston. In the process, the temperature of the gas drops from 1150 K to 400 K. How much work does the gas do?a) Consider a process involving an ideal diatomic gas with n = 3mol, following p = aV, where a = 1 x 105 Pa/m³ is a constant. The gas ex- pands from volume V; = 1 m³ to V; = 4m3. P2 Find the (i) work done on the gas. (ii) heat entering the gas. 1 (iii) change in the internal energy of the gas. b) Now consider the cycle depicted in the figure, involving the same amount of gas as in the previous part. A → B is the process described in the previous subtask, B → C an isochor and C → A an isobar. Additionally, V2/V1 = n = 4 and Vi = 1 m³. Find the Pi 3 i) work done by the gas during one loop of the cycle. V1 V2 V ii) thermal efficiency of the cycle. iii) maximum theoretical efficiency of a Car- not cycle having the same temperature extrema as in this cycle. iv) coefficient of performance of the cycle, if it were used as a refrigerator .One mole of an ideal gas, for which CV,m = 3/2R, initially at 298 K and 1.00 × 10^5 Pa undergoes a reversible adiabatic compression. At the end of the process, the pressure is 1.00 × 10^6 Pa. Calculate the final temperature of the gas. Calculate q, w, ΔU, and ΔH for this process.