Question

the temperature of a rigid (i.e constant volume) sealed container of gas increases from 100 C to 200 C the gas pressure increases by a factor of

Answer 1

Answer:

The pressure increases by a factor of 1.27

Explanation:

From the question given above, the following data were obtained:

Initial temperature (T₁) = 100 °C

Final temperature (T₂) = 200 °C

Initial pressure (P₁) = P

Final pressure (P₂) =?

NOTE: The volume is constant.

Next, we shall convert celsius temperature to Kelvin temperature. This can be obtained as follow:

T(K) = T(°C) + 273

Initial temperature (T₁) = 100 °C

Initial temperature (T₁) = 100 °C + 273

Initial temperature (T₁) = 373 K

Final temperature (T₂) = 200 °C

Final temperature (T₂) = 200 °C + 273

Final temperature (T₂) = 473 K

Next, we shall determine the final pressure of the gas. This can be obtained as follow:

Initial temperature (T₁) = 373 K

Final temperature (T₂) = 473 K

Initial pressure (P₁) = P

Final pressure (P₂) =?

P₁ / T₁ = P₂ / T₂

P / 373 = P₂ / 473

Cross multiply

373 × P₂ = P × 473

Divide both side by 373

P₂ = P × 473 / 373

P₂ = 1.27 × P

Finally, we shall determine the factor by which the pressure of the gas increase as follow:

Initial pressure (P₁) = P

Final pressure (P₂) = 1.27 × P

From the above, we can see that the pressure increased by a factor of 1.27