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Question

The volume (V) versus temperature (T) graph of an ideal gas of given mass, undergoing a thermodynamic process is shown below. During this process, if the temperature increases, then the pressure of the gas

A
first increases then decreases
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B
continuously decreases
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C
continuously increases
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D
first decreases then increases
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Solution

The correct option is B continuously decreases
By Extrapolating the given graph we get,
V=mTc ..........(1)
Here, m is the slope of straight line and c is the negative y intercept.

From the ideal gas equation,
PV=nRT
we can write that,
P=nRTV
P=nRTmTc [from (1)]
P=nRmcT
From this, we can see that, as T increases, cT decreases, (mcT) increases, hence, P decreases.
Therefore, pressure decreases continuously as temperature increases continuously in the given thermodynamic process.
Thus, option (b) is the correct answer.

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