Question

At a constant temperature, a gas is at a pressure of 1080 mm Hg. If the volume is decreased to 40%, find the new pressure of the gas.​

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

GiveN:

• Initial gas at press. = 1080 mm of Hg
• Volume decreased to 40%

[ At a constant temperature ]

To FinD:

• New pressure of the gas....?

Step-by-Step Explanation:

Let the initial volume be V

Then final volume will be 40% of V = 0.4 V

Now, as the temperature is constant here. We can use Boyle' law which says about the relationship between the pressure and volume of a gas.

Boyle's law:

$\because \boxed{ \rm{P_1V_1 = P_2V_2}}$

Here,

• P1 = Initial pres. of the gas = 1080 mm of Hg
• V1 = Initial vol. of the gas = V
• V2 = Final vol. of the gas = 0.4 V

Plugging the values in the formula,

⇒ 1080 × V = P2 × 0.4 V

⇒ 1080 / P2 = 0.4 V/V

⇒ 1080 / P2 = 0.4

⇒ P2 = 1080 / 0.4

⇒ P2 = 10800 / 4

⇒ P2 = 2700 mm of Hg

Thus, the final pres. of the gas will be 2700 mm of Hg.

Answer 2

$\begin{array}{l}P_{1} V_{1}=P_{2} V_{2} \\\\P_{1}=1080 \\\\P_{2}=? \\\\V_{1}=y \\\\V_{2}=0.4 y \\\\1080 \times y=P_{2} \times 0.4 y \\\\\boxed{\sf{P_{2}=\dfrac{1080}{0.4}=2700 \mathrm{mmh} g}}\end{array}$