Question

how much increase in temperature is necessary to increase in Volume of half liter of the gas by 40% at 25 degree celcius keeping the pressure constant​

Answer 1

Answer:-

Given:

Initial Temperature of a gas (T₁) = 25° C = 25 + 273 = 298° K

Volume of the gas increases by 40% by increase in its temperature.

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

→ Final Volume (V₂) = V * (100 + 40/100) = 140V/100 L.

We know that,

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

→ V ∝ kT (k is Constant)

→ V/T = k

⟶ V₁/T₁ = V₂/T₂

Hence,

⟶ V/298 = (140V/100) / T₂

⟶ V * T₂ = 298 * 140V/100

⟶ T₂ = 298 * 140V/100 * 1/V

⟶ T₂ = 417.2° K

Now,

We have to find the increase in the temperature :

Let the % increase be x %.

Hence,

⟶ 298 * (100 + x)/100 = 417.2

⟶ 100 + x = 417.2 * 100/298

⟶ 100 + x = 140

⟶ x = 140 - 100

⟶ x = 40%

Therefore, if the volume of the gas increases by 40% , temperature also increases by 40%.