The volume V of a given mass of a gas varies directly as the temperature T and inversely as the pressure P.? If V=200 cm^3, T=40 degree and P=10 kg/cm^2, how do you find the volume when T=30 degree, P=5kg/cm^2?

Jul 14, 2017

The volume of gas is $300 c {m}^{3}$

Explanation:

$V \propto T , V \propto \frac{1}{P}$. Jointly $V \propto \frac{T}{P} \mathmr{and} V = k \cdot \frac{T}{P}$, k is

proporionality constant. $V = 200 , T = 40 , P = 10$

$V = k \cdot \frac{T}{P} \mathmr{and} k = \frac{P V}{T} = \frac{10 \cdot 200}{40} = 50 \mathmr{and} k = 50$

 T=30 , P=5 , V= ?

The $P , V , T$ equation is $V = k \cdot \frac{T}{P} \mathmr{and} V = 50 \cdot \frac{30}{5} = 300 c {m}^{3}$

The volume of gas is $300 c {m}^{3}$ [Ans]