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.
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- 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…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.
- A diatomic ideal gas at pressure p and volume V is expanding to three times its initial volume under constant pressure. W=2pV. a) If the initial temperature equals T, express the final temperature Tf in terms of the original temperature T. b) In terms of p and V, calculate the expression of the heat Q flowing into the gas. c) In terms of p and V, calculate the expression of the change in internal energy ΔU.The ratio of the molar specific heat capacity at constant pressure to that at constant volume,gamma, for diatomic hydrogen gas is 7/5. In an adiabatic compression, the gas, originally atatmospheric pressure, is compressed from an original volume of 0.30 m3 to 0.10 m3. What is thefinal pressure of the gas?Give the temperature T of 1 mole of ideal gas as a function of the pressure P, volume V, and the gas constant R and give the internal energy U of a rigid diatomic ideal gas as a function of its temperature T and the gas constant R.
- Using the ideal gas law, PV = nRT, determine the volume 200 lbs of hydrogen would occupy at 180 degrees F and a pressure of 100 psig? Assume the constant “R” is 10.731 Ft3PSIA/0R lb mole and the molecular weight of H2 is 2 lbs./mole.A 1.00 mol sample of an ideal diatomic gas, originally at 1.00 atm and 20 oC, expands adiabatically to 1.75 times its initial volume. What are the final pressure and temperature for the gas? ( Assume no molecular vibration)ILLUSTRATE THE PROBLEM ONLY!!! 5 moles of cinnamaldehyde gas that has an initial volume of ten liters expands under the following conditions: 185°F and 800mmHg external pressure. a. How much work is done? Express your answer in L atm. b. Assuming that the container is cylindrical with a base radius of 10cm and can only expand vertically, how much kinetic energy does a single molecule possesses if it travels from base to base of the expanded cylinder in 10μs? Express your answer in J. ILLUSTRATE THE PROBLEM ONLY!!!
- A 1.25 mole sample of an ideal gas is expandedfrom 320. K and an initial pressure of 3.10 bar to a finalpressure of 1.00 bar, and CP, m = 5R/2. Calculate w forthe following two cascs:Condition: The expansion is isothermal and reversible.Does the internal energy (U) of a perfect gas go up or down with increasing pressure under adiabatic, reversible conditions (i.e. at constant entropy)? Hint: you’re looking for ∂U/∂P)s . and under conditions of constant entropy, the transition must be adiabatic and reversible. As such: ∂U= CV ∂T, and ∂T/∂P )s = V/CpIf 9.50 moles of a monatomic ideal gas at atemperature of 235 K are expanded isothermally from a volumeof 1.12 L to a volume of 4.33 L, calculate (a) the work done and while the system performs 120 J of work on its surroundings. Howmuch heat was added to the system?