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=160 cm3 when T=320 kelvin and P=12 kg/cm2. Find the volume when T=240 kelvin and P=16 kg/cm2

Answer 1

Answer:

Volume = 90 cm³

Step-by-step explanation:

Given:

The volume 'V' of a fixed amount of gas is directly proportional to the temperature 'T' and inversely proportional to the pressure 'P'.

Initial volume is, $V_1=160\ cm^3$

Initial temperature is, $T_1=320\ K$

Initial pressure is, $P_1=12\ kg/cm^2$

Final temperature is, $T_2=240\ K$

Final pressure is, $P_2=16\ kg/cm^2$

Final volume is, $V_2=?$

As per question:

$V\propto\frac{T}{P}$

Therefore,

$\frac{PV}{T}=Constant$

Or, we can write the above as:

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\\\\\frac{12\times 160}{320}=\frac{16\times V_1}{240}\\\\6=\frac{V_1}{15}\\\\V_1=15\times 6=90\ cm^3$

Therefore, the final volume is 90 cm³.