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- Show that for an ideal gas _ c p = _ c v + Ru.In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat. Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5. Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas. Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion. Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0. p(V) = __________In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat. Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5. Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas. A) Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion. Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0. p(V) = __________ B) At the end of the adiabatic expansion, the gas fills a new volume V1, where V1>V0. Find W, the work done by the gas on the container during the expansion. Express the work in terms of p0, V0, and V1. Your…
- The only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. Using the results from the discussion of kinetic theory in Section 10.5, show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as U = 3/2PVFor an ideal gas held at room temperature (293 K), if the pressure is changed from 2 atm to 8 atm, the volume wil quadruple double stay the same be 1/4 as muchThe volume of a monatomic ideal gas triples in an isothermalexpansion. By what factor does its pressure change?
- A rigid tank of volume V = 0.02 m3 contains carbon monoxide at a temperature of T0 = 25° C and a pressure of P0 = 9.00 × 105 Pa. This molecule should be treated as a diatomic ideal gas with active vibrational modes. a)The temperature of the gas increases by 10° C. Calculate the pressure of the gas in pascal at this increased temperature. b)Calculate the change to the internal energy of the gas in joules. c)Calculate the change in the entropy of the gas in joules per kelvin.So each four dot shows four different states for an ideal gas. P is the pressure and the other one is the density of the gas. Is temperature of state 1 less or greater than the state 2? Can you please explain why?Calculate the Helmholtz free energy (∆A) of an ideal gas when 2.0 mol expands isothermally from 1.5 to 3.5 cm3 at 120°C
- One mole of the ideal gas is initially at 3 atmand 6 L. As the gas is slowly heated, theplot of its state on a P V diagram moves in astraight line to the state 7 atm and 7 L.Find the work done by the gas.Answer in units of kJ.How would I derive the product PV for a gas of photons in relation to their total internal energy? Given E=hv and p=hv/cUnder what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?