Three processes are performed on a gas from a state given by (p_1, V_1) to a state given by (p_2, V_2) :
a) an isochoric process followed by an isobaric process,
b) an isobaric process followed by an isochoric process,
c) a process where p V remains constant.
Compute for the three processes the work performed on the gas from the initial to the final state. These processes are assumed to be reversible. Determine the analytical results first, then give numerical values in joules.
Numerical Application:
p_1 = p_0 = 1 bar, V_1 = 3 V_0, p_2 = 3 p_0, V_2 = V_0 = 1 l.
Question 2.2: Three processes are performed on a gas from a state given by...
There is no work performed on the gas during an isochoric process, only during the isobaric process or during the process where p V remains constant.
a) The work performed on the gas by an isochoric process followed by an isobaric process is given by,
= −3 p_0 (3 V_0 − V_0) = 6 p_0 V_0 = 600 J.
b) The work performed on the gas by an isobaric process followed by an isochoric process is given by,
W = -\int_{V_1}^{V_2}{p dV} = -p_1\int_{V_1}^{V_2}{dV} = -P_0\int_{3V_0}^{V_0}{dV}= −p_0 (3 V_0 − V_0) = 2 p_0 V_0 = 200 J.
c) The work performed on the gas by a process where pV remains constant, i.e. pV = p_1 V_1 = const, is given by,
W = -\int_{V_1}^{V_2}{p dV} = -p_1V_1\int_{V_1}^{V_2}{\frac{dV}{V} } = -3P_0V_0\int_{3V_0}^{V_0}{\frac{dV}{V}}= −3 p_0 V_0 \ln \Bigl(\frac{V_0}{3V_0}\Bigr) = 3 p_0 V_0 \ln 3 = 330 J.
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