The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P . Suppose that V= 42 cm^3 . when T = 84 kelvin and P = kg/cm^2 . Find the volume when T=185 kelvin and P = 10 kg/cm^2

Complete question:

The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P . Suppose that V= 42 cm^3 . when T = 84 kelvin and P = 8 kg/cm^2 . Find the volume when T=185 kelvin and P = 10 kg/cm^2

The final volume of the gas is 74 cm³

Explanation:

Given;

initial volume of the gas, V₁ = 42 cm³

initial temperature of the gas, T₁ =  84 kelvin

initial pressure of the gas, P₁ = 8 kg/cm²

final volume of the gas, V₂ = ?

final temperature of the gas, T₂ = 185 kelvin

final pressure of the gas, P₂ = 10 kg/cm²

From the statement given in the question, we formulate mathematical relationship between Volume, V, Temperature, T, and Pressure, P.

V ∝ T ∝ ¹/p

where;

k is constant of proportionality

make k subject of the formula

Therefore, the final volume of the gas is 74 cm³