Question

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一摩尔单原子理想气体经历可逆循环a->b->c->a,如下：ab过程体积不变，压强增大；bc是绝热膨胀，Pb=10.0atm, Vb=1.00E-, Vc=8Vb；ca是等压收缩。求(a)气体吸收的热量；(b)气体释放的热量；(c)气体做的功；(d)整个循环的效率。

英文原题: One mole of a monatomic ideal gas is taken through the reversible cycle shown below. Process bc is an adiabatic expansion, with Pb=10.0atm and Vb=1.00*10^(-3)m^3. Find (a)the energy added to the gas as heat; (b)the energy leaving the gas as heat; (c)the net work done by the gas; (d)the efficiency of the cycle.

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Answer 1

bc绝热过程 p*V^γ = C
pb*Vb^(5/3) = pc*Vc^(5/3) ， 求出：pc = 5/16 atm
(a)气体吸收的热量
ab过程吸热 Qab = 3/2 R (Tb - Tc) = 3/2 (pb*Vb - pc*Vc) = 1472.02 J
(b)气体释放的热量
ca过程放热 Qca = 5/2 R (Ta - Tc) = 5/2 (pa*Va - pa*Vc) = -553.984 J
(c)气体做的功 (待求)
(d)整个循环的效率
η = 1 - │Qca│/Qab = 62.3657%
(c)气体做的功
A = Qab * η = 918.036 J