Question

A bottle contains certain volume of a gas at 27oC. To what temperature must the bottle be subjected so that the

volume of the gas (a) increases by 25% (b) decreases by 25% ? (Pressure remaining constant).​

Answer 1

Answer:-

Given:

Initial Temperature (T1) of the gas = 27° C + 273 ° = 300° K

Let Initial Volume (V1) of the gas be "V".

We have to find:

The temperature (T2) when, volume of the gas (a) increases by 25% and (b) decreases by 25%.

From (a).

Final Volume (V2) of the gas = V * (100 + 25) / 100

→ V2 = V * 125/100

→ V2 = 5V/4

We know that,

Charlie's law of gases states that at constant pressure the Volume. of a gas is directly proportional to it's temperature.

$\sf \implies \: \large{ v \: \: \propto \: \: t}$

→ V/T = K

→ V1 / T1 = V2 / T2

→ V/300 = (5V/4) / T2

On cross multiplication we get,

→ T2* V = 300 * 5V/4

→ T2 * V = 375V

→ T2 = 375V/V

→ T2 = 375° K

→ T2 = 375° - 273°

→ T2 = 102° C

From (b).

Final Volume = V * (100 - 25)/100

→ V2 = V*75/100

→ V2 = 3V/4

Using the same formula,

→ V / 300 = (3V/4) / T2

→ T2 * V = 300 * 3V/4

→ T2 * V = 225V

→ T2 = 225V/V

→ T2 = 225° K

→ T2 = 225 - 273

→ T2 = - 48° C

Hence, the Temperature is

• Increased to 102° C when the Volume is increased by 25%.

• Decreased to - 48° C when the Volume is decreased by 25%.

Answer 2

dqwertttuuiopplkjhfs