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During an experiment, an ideal gas is fo...

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 the P-T diagram is parabola

D

The graph of the above process on the P-T diagram is straight line

Text Solution

Verified by Experts

The correct Answer is:
B
`(P_(2))/(rho)=krArr(P^(2)RT)/(PM)=krArrPT=((kM)/(R))`..... (1)
`(P^(2))/(rho)=(p^(2))/(rho//2)rArrp'=(P)/sqrt(2)` Hence from (1), `T'=Tsqrt(2)`
PT=constant hence P-T curve is a hyparbola.
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Knowledge Check

  • During an experiment, an ideal gas is found to obey a condition Vp^2 = constant. The gas is initially at a temperature (T), pressure (p) and volume (V). The gas expands to volume (4V).

    A
    The pressure of gas changes to `(p)/(2)`
    B
    The temperature of the gas changes to `4 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.

  • During an experiment an idea gas is found to obey an additional gas law VT = constant. The gas is initially at temperature T and pressure P . When it is heated to the temperature 2T , the resulting pressure is

    A
    `2P`
    B
    `P//2`
    C
    `4P`
    D
    `P//4`

  • During experiment an ideal gas is found to obey an additional law VP^(2)= constant. The gas is initially at temperature T and volume V, when it expands to volume 2V, the resulting temperature is

    A
    `(T)/(2)`
    B
    `2T`
    C
    `sqrt(2)T`
    D
    `(T)/(sqrt(2))`