Gas, and the work W done on the gas. W_enw = 2416.2 Q = 2416.2 W = -2416.2 Suppo
ID: 1552976 • Letter: G
Question
Gas, and the work W done on the gas. W_enw = 2416.2 Q = 2416.2 W = -2416.2 Suppose that subsequent to this heating, 1.70 times 10^4 J of thermal energy is removed from the gas isothermally. Find the final volume in terms of the initial volume of the example, v_0. v_f = 3.90 times v_0 Are you expecting the final volume to be larger or smaller than 1.25 V_0? Goal Apply the equations of an ideal (Carnot) engine. A steam engine has a boiler that operates at 5.00 times 10^2 K. The energy from the boiler changes water to steam, which drives the piston. The temperature of the exhaust is that of the outside air, 3.00 times 10^2 K. (a) What is the engine's efficiency if it's an ideal engine? (b) If the 3.50 times 10^3 J of energy is supplied from the boiler, find the energy transferred to the cold reservoir and the work done by the engine on its environment. Strategy This problem requires substitution into two equations, both applicable to a Carnot engine. The first equation relates the ratio Q_c/Q_A to the radio T_c/T_R, and the second gives the Carnot engine efficiency.Explanation / Answer
Q = Wenv = 1.70 *104 J
Initial volume(v1) = 1.25 vo
Temperature(T) = 300 K
Work done is :
Wenv = n R T ln (vf /vo )
ln(vf / vi ) = Wenv / (n R T).
(vf / vI) = exp[Wenv / (n R T)]
vf = vi * exp[Wenv / (n R T)]
= 1.25vo * exp [ 1.70 * 104 J / (5.00 * 8.31 * 300 )]
= 4.88 vo
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