Work done in a weird scenario
This was a question asked in JEE Mains 2020, an engineering exam in India. It's common knowledge for anyone writing the exam that work done is the area under the PV graph. I gave this question to a few friends, and according to few of them, the answer is 48. According to me and few others it should be 68, since there is area under this graph too, which is hidden by the question maker showing that the graph begins from (2,2). To explain the answer 48, some of my friends said you just shift the origin to (2,2), and I believe I have a much better grasp of mathematics, and claimed that that operation is wrong, you are changing the function being plotted in such a scenario. But, I can't seem to be able to convince them to not consider (2,2) as the origin of the graph, as they are changing the values of real life functions.
I also believe, they seem to have difficulty understanding the concept of what origin means. 359
According to them, it refers to the point where both the axes meet. According to me, origin is just the point where both functions are 0. Axes tell you nothing extraordinary, they just help you locate the value a point represents, and map a certain direction to increase or decrease of a function. And axes don't need to be marked from the origin, according to my understanding, they should just help us locate the value of the particular function they correspond to, for a certain point. So at the intersection of the two weird axes stated in the question, the pressure is 2 and volume is 2. Shifting the origin changes the function we plot to Pressure - 2 and Volume - 2 which have no significance with the real life functions.
Could anyone please share a convincing solution for as to why it's 68 (considering the complete view of the graph) or disprove me as to why the answer should be 48 (only the area under graph given)?
Thanks! 229