Boyle’s law may be Written as

Analysis

The question asks for the mathematical representation of Boyle’s Law, which describes the relationship between the pressure and volume of a fixed mass of gas at a constant temperature.

Concept: Boyle’s Law

Boyle’s Law states that for a fixed mass of an ideal gas, the pressure ($P$) is inversely proportional to its volume ($V$), provided the temperature ($T$) remains constant.

Mathematically, this is expressed as: $P \propto \frac{1}{V}$ Which leads to the equation: $PV = k$ (where $k$ is a constant)

When comparing the same gas under two different sets of conditions (state 1 and state 2) at a constant temperature, we equate the constants: $P_1V_1 = P_2V_2$

Step-by-Step Solution

1. Identify the variables: $P$ represents Pressure, $V$ represents Volume.
2. Apply the condition: The law specifies that temperature must be constant.
3. Formulate the relationship: Since $P$ is inversely proportional to $V$, the product of pressure and volume remains constant ($PV = \text{constant}$).
4. Compare states: If the initial state is $(P_1, V_1)$ and the final state is $(P_2, V_2)$, then: $P_1V_1 = P_2V_2$

Reviewing the Options

• A. $P_1V_1 = P_2V_2$: This correctly represents Boyle's Law.
• B. $V_1 = V_2 \div T_1T_2$: This is incorrect and does not represent any standard gas law.
• C. $P_1T_1 = P_2T_2$: This is incorrect; it resembles a variation of Gay-Lussac's Law, but is written incorrectly.
• D. $P_1V_1 \div T_1 = P_1V_1 \div T_2$: This is a distorted version of the General Gas Law (Combined Gas Law).

Exam Tip

To remember the gas laws easily, use the mnemonic "TV-PU-PT":

• T (Temperature) is constant for Boyle's Law ($PV = k$).
• V (Volume) is constant for Pressure Law ($P/T = k$).
• P (Pressure) is constant for Charles's Law ($V/T = k$).