Question

How to solve this ?

Answer 1

The answer is `option (C)`

Explanation:

Apply Boyle's Law

`P_1V_1=P_2V_2` at `" constant temperature "`

The initial pressure is `P_1=P`

The initial volume is `V_1=V`

The final volume is `V_2=1/2V`

The final pressure is

`P_2=V_1/V_2*P_1=V/(1/2V)*P`

`=2P`

The answer is `option (C)`

Answer 2

See below

Explanation:

There is at the very least a typo in this question :(

Assuming that the process is isothermic, then from the ideal gas law:

`pV= p' V' qquad [= nRT = nRT']`

`implies p' = p V /(V') = p V/(V/2) = 2 bb color(red)(p)`

That option is not in the answer key.

More likely in practical terms, the process is adiabatic . In that case:

• `pV^gamma = " const"`

• `implies p' = p (V/(V'))^gamma = p * 2^gamma`

`gamma_("air") = 1.4 implies p' = 2.64 \ bb p`

That answer is definitely not in the answer key, so it seems you are expected to make the assumption that the temperature inside the pump remains constant.