At point A in a Carnot cycle, 2.34 mol of a monatomic ideal gas has a pressure of 1 400 kPa, a volume of 10.0 L, and a temperatu
re of 720 K. The gas expands isothermally to point B and then expands adiabatically to point C, where its volume is 24.0 L. An isothermal compression brings it to point D, where its volume is 15.0 L. An adiabatic process returns the gas to point A. (a) Determine all the unknown pressures, volumes, and temperatures as you fill in the following table. P V T A 1 400 kPa 10.0 L 720 K B C 24 L D 15 L (b) Find the energy added by heat, the work done by the engine, and the change in internal energy for each of the steps A ? B, B ? C, C ? D, and D ? A. Process Q (kJ) W (kJ) ?Eint (kJ) A ? B B ? C C ? D D ? A (c) Calculate the efficiency Wnet / |Qh|. % (d) Show that the efficiency is equal to 1 ? TC / TA, the Carnot efficiency. (Do this on paper. Your instructor may ask you to turn in this work.)
1 answer:
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Answer:
a) T = 2.26 N, b) v = 1.68 m / s
Explanation:
We use Newton's second law
Let's set a reference system where the x-axis is radial and the y-axis is vertical, let's decompose the tension of the string
sin 30 =
cos 30 =
Tₓ = T sin 30
T_y = T cos 30
Y axis
T_y -W = 0
T cos 30 = mg (1)
X axis
Tₓ = m a
they relate it is centripetal
a = v² / r
we substitute
T sin 30 = m (2)
a) we substitute in 1
T =
T =
T = 2.26 N
b) from equation 2
v² =
If we know the length of the string
sin 30 = r / L
r = L sin 30
we substitute
v² =
v² =
For the problem let us take L = 1 m
let's calculate
v =
v = 1.68 m / s