Question

During an experiment, an ideal gas is found to obey a condition `(p^2)/(rho) = "constant"`. (`rho` = density of the gas). The gas is initially at temperature (T), pressure (p) and density `rho`. The gas expands such that density changes to `rho//2`.
A. The pressure of the gas changes to `sqrt(2) p`.
B. The temperature of the gas changes to `sqrt(2) T`
C. The graph of the above process on (p - T) diagram is parabola.
D. The graph of the above process on (p - T) diagram is hyperbola.

Answer 1

Correct Answer - B::D
`p prop sqrt (rho)` as per process. If `rho` becomes half, then (p) will becomes `sqrt (2)` times.
Futher, ` p prop (1) /(V)`
`:. (p^2)/((1//V)) =` constant
or `(pV) p =` constnat
Hence, ` Tp =` constant
`:. p prop (1)/(T)`
or (P - T) graph is a rectangular hyperbola.