Question

which of the following relationships correctly depict the relationship between pressure and volume for a fixed amount of gas at constant temperature according to Boyle’s law.

1. PV∝V
2. P∝V
3. V∝1P
4. P∝1V
5. PV∝P
6. V∝P

Answer 1

Answer:

Non of the option applies

Explanation:

Gases may be assumed to obey the ideal gas law, which states that, for pressure P, volume V, number of moles n, and temperature T,

PV = nRT.

where  R  is the gas constant, and n is the number of mole of gas

If the temperature is held constant, we obtain a simplified version called Boyle's Law, and if the pressure is held constant, we obtain Charles' Law.

Boyle's law:

Boyle's law states that the volume of a given mass of gas is inversely proportional to is pressure, provided that the temperature remains constant.

Mathematically,

P ∝ I/V

∴ PV ∝ 1

From the above mathematical expression, it shows that PV is a constant and does not change with pressure or volume.

∴ non of the options applies

Answer 2

Boyle’s law : $\rm P\propto \dfrac{1}{V}$

Further explanation  

There are several gas equations in various processes:  

• 1. Avogadro's hypothesis  

In the same temperature and pressure, in the same volume conditions, the gas contains the same number of molecules  

So it applies: the ratio of gas volume will be equal to the ratio of gas moles  

$\dfrac{V_1}{V_2}=\dfrac{n_1}{n_2}$

• 2. Boyle's Law  

At a fixed temperature, the gas volume is inversely proportional to the pressure applied  

$\rm p_1V_1=p_2.V_2\\\\\dfrac{p_1}{p_2}=\dfrac{V_2}{V_1}$

• 3. Charles's Law  

When the gas pressure is kept constant, the gas volume is proportional to the temperature  

$\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}$

• 4. Gay Lussac's Law  

When the volume is not changed, the gas pressure in the tube is proportional to its absolute temperature  

$\dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}$

• 5. Law of Boyle-Gay-Lussac  

Combined with Boyle's law and Gay Lussac's law  

$\dfrac{P_1.V_1}{T_1}=\dfrac{P_2.V_2}{T_2}$

P1 = initial gas pressure (N/m² or Pa)  

V1 = initial gas volume (m³)  

P2 = gas end pressure  

V2 = the final volume of gas  

T1 = initial gas temperature (K)  

T2 = gas end temperature  

Can be concluded  

Boyle's law at constant T,  

$\large{\boxed{\bold{P\propto\:\frac{1}{V}\Rightarrow PV=k}}}$

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Keywords : constant temperature,Boyle’s law,pressure, volume