BE SURE ANSWER IS IN THE CORRECT UNITS! Thank you for your help An ideal gas initially at P;, Vi, and T; is taken through a cycle as shown below. (Let the factor n = 3.1.)PВnP;P;ATDnV;(a) Find the net work done on the gas per cycle for 1.20 mol of gas initially at 0°C.kJ(b) What is the net energy added by heat to the system per cycle?kJ

Answered: An ideal gas initially at P, V, and T;…

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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BE SURE ANSWER IS IN THE CORRECT UNITS! Thank you for your help

An ideal gas initially at P;, Vi, and T; is taken through a cycle as shown below. (Let the factor n = 3.1.)
P
В
nP;
P;
AT
D
nV;
(a) Find the net work done on the gas per cycle for 1.20 mol of gas initially at 0°C.
kJ
(b) What is the net energy added by heat to the system per cycle?
kJ

Expert Solution

Part A:

Area enclosed by the cycle in P-V coordinates gives the net work interaction for the gas.

If the cycle is a clockwise cycle , net work is done by the gas.

If the cycle is a counterclockwise cycle , net work is done on the gas.

Here the cycle is clockwise ,so net work is done by the gas.

Net work done by the gas =Area enclosed by the cycle

$Area Enclosed by the cycle = Area of the square formed by ABCD Area Enclosed by the cycle = ({nP}_{i} - P_{i}) ({nV}_{i} - V_{i}) = {(n - 1)}^{2} (P_{i} V_{i}) = {(3.1 - 1)}^{2} P_{i} V_{i} = 4.41 P_{i} V_{i} - - - - Equation (1) From ideal gas equation, we have, P_{i} V_{i} = {nRT}_{i} given initial temperature T_{i} = 0^{0} C = 273 K P_{i} V_{i} = 1.2 \times 8.314 \times 273 = 2723.6664 From Equation (1) Area Enclosed by the cycle = 4.41 P_{i} V_{i} = 4.41 \times 2723.6664 = 12011.36 Net work done by the gas = 12011.36 J = 12.011 kJ$

Since the question to find the net work done on the gas per cycle it will have opposite sign.

Therefore , net work done on the gas = -12.011kJ

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