Question

at0°C and 760 mm Hg pressure, a gas occupies a volume of 100cm³. the kelvin temperature(absolute temperature)of gas is increased by one-fifth while the pressure is increased one and a half times.Calculate the final volume of the gas. {HINT:answer is 80cc}

Answer 1

please see this picture

Answer 2

Given:

• Temperature($T_1$) = 0°C = 273 K
• Volume($V_1$) = 100 $cm^3$
• Pressure($P_1$) = 760 mm Hg

To Find:

• The final volume of the gas. ($V_2$)

Solution:

1) It is given that the kelvin temperature of the gas is increased by one-fifth.

∴ $T_2$ =  273 + 273/5  {taking LCM}

$T_2$  = (1365+273)/5  {adding and multiplying}

$T_2$  = 1638/5 = 327.6 K

2) It is given that the pressure of the gas is increased by one and a half times.

∴$P_2$ = 760 +760/2 {taking LCM}

∴$P_2$  = (1520+760)/2 {adding and multiplying}

∴$P_2$  = 2280/2 = 1140 mm Hg

Now we are going to find the final volume ($V_2$),

The formula is given by,

$\frac{P_1*V_1}{T_1} =\frac{P_2*V_2}{T_2}$ → {equation 1}

On substituting the values in equation 1 we get,

⇒ (760×100)/273 = (1140×$V_2$)/327.6 {multiplying the terms}

⇒ 76000/273 = 1140$V_2$/327.6 {dividing the terms in LHS}

⇒ 278.38 = 1140$V_2$/327.6 {cross-multiplying}

⇒ 91197.28 = 1140$V_2$  

⇒ $V_2$ = 91197.6/1140  {dividing the terms}

⇒ $V_2$ = 79.99 ~ 80 $cm^3$

∴ The final volume of the gas ($V_2$) = 80 $cm^3$