Question

A gas is compressed by an adiabatic process that decreases its volume by a factor of 2.
In this process, the pressure
In this process, the pressure
a) increases by a factor of more than 2.
b) increases by a factor of 2.
c) does not change.
d) increases by a factor of less than 2.

Answer 1

Answer

OPTION A is correct

a)increases by a factor of more than 2.

Explanation:

adiabatic process is a process that takes place without the transfer of heat or mass between a thermodynamic system and its surroundings.

It is a process in which no heat transfer takes place. It does not denote that the temperature is constant.

Then from an adiabatic system,

we know that

PV= constant

PV^γ= constant

γ=ratio of specific heat for the gas

Where P= pressure of the system

V= volume of the system

We can say P= 1/(V^γ)

Where γ >1

Which means the pressure is inversely proportional to the volume raise to power of gamma sign and whenever the pressure increases the volume decreases with V^γ.

The question says the volume is decreased by factor of two then V^γ will also decreased by factor of 2.

That means (2^γ) > 2

Since our γ > 1 Therefore, the pressure increases by a factor of more than 2.

Answer 2

Answer:

a) increases by a factor of more than 2.

Explanation:

In an adiabatic process,

$PV^{Y} = constant$

we can say that the volume is inverse to the pressure as

$V^{Y}$∝ $\frac{1}{P}$

where

$P$ is the pressure

$V$ is the volume

$Y$ is the adiabatic index, and it is always greater than 1

If volume V is decreased by a factor of 2, then it is actually decreased by a factor of $2^{Y}$ in proportion to the pressure, and since $Y$ is always greater than 1, it is actually decreased by a factor greater than 2 in proportion to the pressure.

This means that the pressure will also increase by a factor greater than 2.