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Elden [556K]
3 years ago
10

A gas undergoes a process in a piston–cylinder assembly during which the pressure-specific volume relation is pv1.1 = constant.

The mass of the gas is 0.4 lb and the following data are known: p1 = 160 lbf/in.2, V1 = 1 ft3, and p2 = 300 lbf/in.2 During the process, heat transfer from the gas is 2.1 Btu. Kinetic and potential energy effects are negligible. Determine the change in specific internal energy of the gas, in Btu/lb.
Physics
1 answer:
Sati [7]3 years ago
8 0

Answer:

\Delta u = 53.99 Btu/lbm

Explanation:

given data:

P_1 = 160 lbf/in^2 = 23040 lbf/ft^2

P_2 = 300 lbf/in^2 = 56160 lbf/ft^2

V_1 = 1ft^3

Q = - 2.1 Btu

PV^{1.1} = constant

P_1V_1^{1.1} = P_2V_2^{1.1}

V_2 = V_1 [\frac{P_1}{P_2}]^{1.1}

       =  1 [\frac{23040}{56160}]^{\frac{1}{1.1}

       = 0.44 ft^3

work done during polytropic process

w = \frac{P_2V_2 - P_1V_1}{1-n}

   = \frac{56160 \times 0.4759 - 23040\times 1}{1 - 1.2}

   = -18442.1 ft lbf

we know 1 Btu = 778.169 ft. lbf, therefore

w = -23.6993 Btu

Q = W + m\Delta u

-2.1 = - 23.6993 + 0.4 \Delta u

\Delta u = 53.99 Btu/lbm

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