question_answer

A gas at pressure \[6\times {{10}^{5}}N\text{/}{{m}^{2}}\]and volume 1 m3 expands to \[3\,{{m}^{3}}\] and its pressure falls to\[4\times {{10}^{5}}N\text{/}{{m}^{2}}\]. Given that the indicator diagram is a straight line, work done by the system is

A)  \[6\times {{10}^{5}}J\]                 

B)  \[3\times {{10}^{5}}J\]

C)  \[4\times {{10}^{5}}J\]                 

D)  \[10\times {{10}^{5}}J\]

E)  None of these

Correct Answer: D

Solution :

                The indicator diagram can be shown as below. Work done by the system = area under p-V diagram = area of rectangle BCDE + area of\[\Delta \]ABC \[=4\times {{10}^{5}}\times 2+\frac{2\times {{10}^{5}}\times 2}{2}\] \[=8\times {{10}^{5}}+2\times {{10}^{5}}\] \[=10\times {{10}^{5}}J\]