The volume V of gas varies inversely as the pressure P on it. The volume of a gas is 200 cm^3 under a pressure of 21 kg/cm^2. What will it's volume under a pressure of 30/kg/cm^2?

Question

Avery Adams · Accepted Answer

140 #cm^2#

Boyle's law states that for a fixed mass of gas at constant temperature, the absolute pressure and the volume of a gas are inversely proportional. #p1*v1 =p2*v2#

So, #p1*v1 =p2*v2# 21 kg/#cm^2# × 200 #cm^3# = 30 kg/#cm^2#× v2

v2 is equal to 140 cm^2.

Henry Antrim · Answer

undefined Using the inverse variation relationship $ V \propto \frac{1}{P} $, we can set up the equation $ V_1 \cdot P_1 = V_2 \cdot P_2 $, where $ V_1 $ and $ P_1 $ are the initial volume and pressure, and $ V_2 $ and $ P_2 $ are the final volume and pressure.

Given:
$ V_1 = 200 \text{ cm}^3 $, $ P_1 = 21 \text{ kg/cm}^2 $, and $ P_2 = 30 \text{ kg/cm}^2 $.

Using the equation:
$ 200 \cdot 21 = V_2 \cdot 30 $.

Solving for $ V_2 $:
$ V_2 = \frac{200 \cdot 21}{30} $,
$ V_2 = 140 \text{ cm}^3 $.

Therefore, the volume of the gas under a pressure of $ 30 \text{ kg/cm}^2 $ will be $ 140 \text{ cm}^3 $.