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- A monatomic ideal gas undergoes a quasi-static process that is described by the function pV=p1+3(vv1) , where the stating state is (p1,v1) and the final state (p2,v2) . Assume the system consists of n moles of the gas in a container that can exchange heat with the environment and whose volume can change freely. (a) Evaluate the work done by the gas during the change in the state. (b) Find the change in internal energy of the gas. (c) Find the heat input to the gas during the change. (d) What ale initial and final temperatures?With the help of the two preceding problems, show that S between states 1 and 2 of nmoles an ideal gas is given by S=CnplnT2T1nRlnP2P1.Derive a formula for the coefficient of performance of a refrigerator using an ideal gas as a working substance operating in the cycle shown below in terms of the properties of the three states labeled 1, 2, and 3.
- (a) A 5.0-kg rock at a temperature of 20 is dropped into a shallow lake also at 20 from a height of 1.0103 m. What is the resulting change in entropy of the universe? (b) If the temperature of the lock is 100 when it is dropped, what is the change of entropy of the universe? Assume that air friction is negligible (not a good assumption) and that c=860 J/kg K is the specific heat of the rock.In an isothermal reversible expansion at 27 , an ideal gas does 20 J of work. What is the entropy change of the gas?The temperature of n moles of an ideal gas changes from T1 to T2 in a quasi-static adiabatic transition. Show that the work done by the gas is given by W=nR1(T1T2).
- Two moles of a monatomic ideal gas such as oxygen is compressed adiabatically and reversibly from a state (3 atm, 5 L) to a state with a pressure of 4 atm. (a) Find the volume and temperature of the final state. (b) Find the temperature of the initial state. (c) Find work done by the gas in the process. (d) Find the change in internal energy in the process. Assume Cv=5R and Cp=Cv+R for the diatomic ideal gas in the conditions given.Statistical mechanics says that in a gas maintained at a constant temperature through thermal contact with a bigger system (a "reservoir") at that temperature, the fluctuations in internal energy are typically a fraction 1/N of the internal energy. As a fraction of the total internal energy of a mole of gas, how big are the fluctuations in the internal energy? Are we justified in ignoring them?a box of mass 10.0 kg and intaial velocity 3.0 m/s slides along a floor and comes to a rest due to friction. estimate the total cahnge in entropy of the universe. assume everthing occures at room tempeture of 293 k
- According to the Debye equation the heatthe capacity of a solid is proportional to the temperaturecubed at low temperatures, Cp(T) = σT3, where σis a constant. Show that the entropy at a temperatureT0 is given by S(T0) = Cp(T0)/3 when the Debyeequation holds.Quuz The PV diaspam belom shone (AB,&C etc) applied Tengle engine. a sequence of gar OroceRs to an ideal ins tde an B isothermal compression ? does the peesure increase with 1ikhich process is an 2' Ln nluch constant volumé 3: In which if• Khat is the work done DA ? 5.im whuch proces is nork fone the Ly on the gas in the protefs. procers g8s in fhe gas ther meady namrz system the wexpctes. syoten exprates.com for work done at Eonstant pressure tind vélume change is qiven by an ideal gas (the internal t6. In adiababie expansion, of an a work of 255 is done klhat 7 is energy of the Tes 7. Winte the Ynamizs for the first Law of thermd- eepresion-Consider a lassi cal ideal gas Consisting of N atoms of mass M in thermal bniem at anprete T, miving in a equile 3 dimensional 4bnum harmonic potenhal Well. mutr? 2 2. v(r)s a. Cal culate The par n'tion funchm of The system. b.Compute the average energy of the Sy stem C. Comprute The entropy of the system,