There are 2. 34 moles of monoatomic ideal gas with a pressure of 1400 kPa, volum

Question

There are 2. 34 moles of monoatomic ideal gas with a pressure of 1400 kPa, volume of 10. 0 L and a temperature of 720. K at point A in a Carnot cycle. The gas expands isothermally to point B. Next it expands adiabatically to a volume of 24. 0 L at point C. This is followed by isothermal compression to point D (with a volume of 15. 0 L) and, finally, by an adiabatic process that returns the gas to point A. (a) Fill in the table. (b) Find the energy added by heat, the work done, and the change in the internal energy for each of the following steps: A to B, B to C, C to D and D to A. (c) Show that Wnet/Qm = 1- Tc/ TA, the Carnot efficiency.

Explanation / Answer

In physics and chemistry, monatomic is a combination of the words "mono" and "atomic," and means "sinole atom." It is usually applied to gases: a monatomic gas is one in which atoms are not bound to each other. All elements will be monatomic in the gas phase at sufficiently high temperatures. At standard temperature and pressure (STP), all of the noble gases are monatomic. These are helium, neon, argon, krypton, xenon and radon. The heavier noble gases can form compounds, but the lighter ones are unreactive. Monatomic hydrogen comprises about 75% of the elemental mass of the universe.[1] The motion of a monatomic gas is translation (electronic excitation is not important at room temperature). Thus in an adiabatic process, monatomic gases have an idealised ?-factor (Cp/Cv) of 5/3, as opposed to 7/5 for ideal diatomic gases where rotation (but not vibration at room temperature) also contributes. Also, for ideal monatomic gases: the molar heat capacity at constant pressure (Cp) is 5/2 R = 20.8 J?K-1?mol-1 (4.97 cal?K-1?mol-1); the molar heat capacity at constant volume (Cv) is 3/2 R = 12.5 J?K-1?mol-1 (2.98 cal?K-1?mol-1); where R is the gas constant.

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