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# HW4_key - HW4_Chapter 19 19-2 Q Consider an ideal gas that...

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HW4_Chapter 19 19-2: Q. Consider an ideal gas that occupies 2.50 dm 3 at a pressure of 3.00 bar. If the gas is compressed isothermally at a constant external pressure, P ext , so that the final volume is 0.500 dm 3 , calculate the smallest value P ext can have. Calculate the work involved using this value of P ext . A. Since the gas is ideal, we can write 3 1 1 2 3 2 (3.00 )(2.5 ) 15.0 0.500 PV bar dm P bar V dm The smallest possible value of P ext is P 2 . The work done in this case is (Equation 19.1) 1 1 3 3 1 1 8.3145 (15.0 )( 2.0 ) 3000 0.083145 ext J mol K w P V bar dm J bar dm mol K     19-6: Q. Calculate the minimum amount of work required to compress 5.00 moles of an ideal gas isothermally at 300 K from a volume of 100 dm 3 to 40.0 dm 3 . A. We note that the minimum amount of work required is the amount of work needed to reversibly compress the gas, so we can write Equation 19.2 as 2 min 1 ln rev V w w nRT V   1 1 (5.00 )(8.315 )(300 )ln0.4 11.4 mol J mol K K kJ   19-17: Q. Show that / 2 2 1 1 P R C T P T P for a reversible adiabatic expansion of an ideal gas. A. For an ideal gas, V P C R C and

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