Question

1. Consider the example problem, but with the lower pressure reduced to 100 Pa. How much work would be done in a single cycle?1. 29,970 J2. 0 J3. -30,030 J4. 27,000 J

Answer 1

Answer:

29970 J

Step-by-step explanation:

Given:

`\begin{gathered} P_A=P_B=10^5Pa \\ P_c=P_D=100\text{ Pa\lparen The new lower pressure\rparen} \\ V_A=V_D=0.1m^3 \\ V_B=V_C=0.4m^3 \end{gathered}`

Work done across AB

`\begin{gathered} W_(AB)=P_(AB)(V_B-V_A) \\ \\ W_(AB)=10^5(0.4-0.1) \\ \\ W_(AB)=0.3*10^5 \\ \\ W_(AB)=30000J \end{gathered}`

Work done across BC = 0 J (Since there is no change in volume)

Work done across DA = 0 J (Since there is no change in volume)

Work done across CD

`\begin{gathered} W_(CD)=P_(CD)(V_D-V_C) \\ \\ W_(CD)=100(0.1-0.4) \\ \\ W_(CD)=100(-0.3) \\ \\ W_(CD)=-30J \end{gathered}`

Work done in one cycle:

`\begin{gathered} W_(cycle)=W_(AB)+W_(BC)+W_(DA)+W_(CD) \\ \\ W_(cycle)=3000J+0+0-30 \\ \\ W_(cycle)=29970J \end{gathered}`

29970J of work will be done in a single cycle