In a cylinder, 1.20 mol of an ideal monatomic gas, initially at and 300 K, expands until its volume triples. Compute the work done by the gas if the expansion is (a) isothermal; (b) adiabatic; (c) isobaric. (d) Show each process in a pV-diagram. In which case is the absolute value of the work done by the gas greatest? Least? (e) In which case is the absolute value of the heat transfer greatest? Least? (f) In which case is the absolute value of the change in internal energy of the gas greatest? Least?
We are given an ideal monatomic gas with a number of moles = 1.20 mol at initial pressure and initial temperature = 300 K. The gas expands until its volume triples which means . We want to calculate the work done of the process if the expansion is (a) isothermal, (b) adiabatic, and (c) isobaric.
(a) Isothermal process means the temperature is constant during the process where = 0 while the pressure and the volume are changed. So the work done for the isothermal process is given by
Where could be extracted from ideal gas law by . Now plug this value of into equation (1) and take the constant term outside the integration and complete the integration where equation (1) will be
Now we can plug our values for and into equation (1*) to get the work done during the isothermal process where is the gas constant and equals (See Appendix F) and
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As a budding mechanical engineer, you are called upon to design a Carnot engine that has 2.00 mol of a monatomic ideal gas as its working substance and operates from a high- temperature reservoir at . The engine is to lift a 15.0-kg weight 2.00 m per cycle, using 500 J of heat input. The gas in the engine chamber can have a minimum volume of 5.00 L during the cycle.
Draw a pV-diagram for this cycle. Show in your diagram where heat enters and leaves the gas.
Two moles of an ideal gas occupy a volume V. The gas expands isothermally and reversibly to a volume 3 V. (a) Is the velocity distribution changed by the isothermal expansion? Explain. (b) Use Equation to calculate the change in entropy of the gas. (c) Use Equation to calculate the change in entropy of the gas. Compare this result to that obtained in part (b).