A sample of of an ideal monatomic gas executes the four-step closed cycle described below

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

A sample of

n = 0.10\,\text{mol}

of an ideal monatomic gas executes the four-step closed cycle described below. Numerical data are given in the table; blank cells indicate quantities to be found. Use the convention that work done on the gas and energy transferred into the gas by heating are positive. STATE DATA Step Process

P

(Pa)

V

(\text{m}^3)

W

(J)

Q

(J)

\Delta U

(J) 1 Isobaric expansion

1.5\times10^{5}

0.001\;\rightarrow\;0.002

? ? ? 2 Isochoric pressurization

1.5\times10^{5}\;\rightarrow\;2.5\times10^{5}

0.002

0 ? ? 3 Isobaric compression

2.5\times10^{5}

0.002\;\rightarrow\;0.001

? ? ? 4 Isochoric cooling

2.5\times10^{5}\;\rightarrow\;1.5\times10^{5}

0.001

0 ? ? (The universal gas constant is

R = 8.31\,\text{J mol}^{-1}\text{K}^{-1}

.) (a) Calculate the work, the change in internal energy, and the energy transferred by heating for step 1. (b) Determine the change in internal energy and the energy transferred by heating for step 2. (c) Compute the work, change in internal energy, and energy transferred by heating for step 3. (d) Determine the change in internal energy and the energy transferred by heating for step 4. (e) Using your results, find the net work done on the gas and the net energy transferred by heating for the entire cycle. Verify that these quantities are consistent with the first law of thermodynamics for a closed cycle.

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