Question

A gas X having a volume of 1 litre at 10°C is heated. It's
volume changes to 3 litres on heating and the pressure is
simultaneously tripled. Calculate the new temperature required
for the change.​

Answer 1

Given:-

→ Initial volume = 1 L = 1000 mL

→ Initial temperature = 10°C

→ Final volume = 3 L = 3000 mL

→ Final pressure is thrice the initial

pressure.

To find:-

→ New temperature / Final temeprature

Solution:-

Firstly, let's convert the initial temperature from °C to K.

=> 0°C = 273 K

=> 10°C = 273 + 10

=> 283 K

Let the initial pressure be P₁ and final pressure be P₂. Now according to the question, the final pressure is thrice the initial pressure.

∴ P₂ = 3P₁

Now according to Combined Gas Law :-

P₁V₁/T₁ = P₂V₂/T₂

Where :-

• P₁ is the initial pressure.

• V₁ is the initial volume of the gas

• T₁ is the initial temperature.

• P₂ is the final pressure.

• V₂ is the final volume of the gas.

• T₂ is the final temperature.

By substituting values, we get :-

=> P₁×1000/283 = 3P₁×3000/T₂

=> 1000P₁/283 = 9000P₁/T₂

=> 1000P₁T₂ = 9000P₁×283

=> 1000P₁T₂ = 2547000P₁

=> T₂ = 2547000P₁/1000P₁

=> T₂ = 2547 K

Thus, the new temperature required for the change is 2547K or 2274°C .