Question

By what factor does the gas temperature change if the volume is doubled and the pressure is tripled?

Answer 1

• If the volume is doubled and the pressure is tripled, the temperature changes by a factor of 6.

Step-by-step explanation:

Since, for ideal gases the temperature is in direct relation to the volume and the pressure, you can predict that if the volume is doubled and the pressure is tripled the effect on the temperature will be 3 × 2 = 6 times.

You can prove it using the combined law of gases:

• P₁ V₁ /T₁ = P₂ V₂ / T₂

Where the letters P denote absolute pressures, the letters T denote temperature measured in absolute scale, and the letters V denote volume.

The changes given may be written it this way:

• V₂ = 2 × V₁ = 2V₁

• P₂ = 3 × P₁ = 3P₁

Then, you can write T₂ in terms of the other variables:

• T₂ = (P₂ V₂ T₂) / (P₁ V₁) = 3P₁ 2V₁ T₂ / (P₁V₁)

Cancel the common factors P₁ and V₁

• T₂ = 6 T₁

Which proves that the final temperature is 6 times the initial temperature.