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(D) For an ideal gas,the temperature $T$ is proportional to the product of pressure and volume,i.e.,$T \propto PV$.Since the process is a straight lin

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Both $(B)$ and $(C)$.

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(D) For an ideal gas,the temperature $T$ is proportional to the product of pressure and volume,i.e.,$T \propto PV$.Since the process is a straight line on the $P-V$ diagram,the equation of the line is $P = -mV + c$,where $m$ is the magnitude of the slope $(m > 0)$ and $c$ is the intercept.Substituting this into the temperature relation: $T \propto (-mV + c)V = -mV^2 + cV$.This is a downward-opening parabola with respect to $V$. The temperature $T$ increases as $V$ increases until it reaches a maximum value at the vertex of the parabola,and then it decreases as $V$ continues to increase.Since the initial and final temperatures are equal,the process must cross different isothermal curves $(T_1, T_2, T_3, T_4)$ such that it starts at a lower temperature,reaches a maximum,and returns to the initial temperature value.Thus,the temperature first increases and then decreases,and the straight line must have a negative slope to intersect the isothermal curves in this manner.

$A$ 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:

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