Question

there is a diagram showing two states of a gas - like system. in the first state, pressure ( p_1 = 25 ), volume ( v_1 = 6 ). in the second state, pressure ( p_2 = 5 ), volume ( v_2 = dots ). also, there is a blank to fill the law name (marked as 7. ______ law).

Explanation:

Step1: Identify the law (Boyle's Law)

This problem involves pressure and volume of a gas, so we use Boyle's Law, which states that for a fixed amount of gas at constant temperature, \( P_1V_1 = P_2V_2 \).

Step2: Substitute the known values

We know \( P_1 = 25 \), \( V_1 = 6 \), and \( P_2 = 5 \). Substitute these into the formula: \( 25 \times 6 = 5 \times V_2 \).

Step3: Solve for \( V_2 \)

First, calculate the left - hand side: \( 25\times6 = 150 \). Then, we have the equation \( 150 = 5V_2 \). To solve for \( V_2 \), divide both sides of the equation by 5: \( V_2=\frac{150}{5}=30 \).

Answer:

The value of \( V_2 \) is 30, and the law is Boyle's Law.