A gas expands such that its initial and final temperatures are equal. Also the process followed by the gas traces a straight line on the `P-V` diagram
(i) The temperature of the gas remains constant throughout
(ii) The temperature of the gas first increases and then decreases
(iii) The temperature of the gas first decreases and then increases
(iv) The straight line has negative slope

Options

A. The temperature of the gas remains constant throughout.
B. The temperature of the gas first increases and then decreases.
C. The temperature of the gas first decreases and then increases.
D. The straight line has a negative slope.

Answer

B, D

Explanation

Let `V_(0)` = initial volume = `2V_(0)` = final volume
V = volume of any state
then `(P_(0)-P_(0)//2)/(2V_(0) - V) = (P-P_(0)//2)/(2V_(0)-V)`
`implies nRT = PV = V[(3P_(0))/(2) - (P_(0))/(2V_(0))V]`
`therefore T'-V` curve is a parabola with vertex above.
Hence temperature first increases then decreases.