Question

If a gas in a closed container is pressurized from 15.0 atmospheres to 16,212 millibars and its original temperature was 25.0 °C, what would the final temperature of the gas be?

Answer 1

The final temperature of the gas when pressurized from 15.0 atmospheres to 16,212 millibars, with an original temperature of 25.0°C, would be approximately 44.95°C.

Step-by-step explanation:

The student's question involves the final temperature of a gas when its pressure is increased in a closed container. To find the answer, we can use the Combined Gas Law which relates pressure (P), volume (V), and temperature (T) in a closed system:

PV / T = constant

Since the volume and amount of gas are constant, we can simplify this to:

P₁ / T₁ = P₂ / T₂

However, we first need to convert the given pressures to the same units. We know that 1 atm = 1013.25 millibars, so:

15.0 atm x 1013.25 millibars/atm = 15198.75 millibars

We also need to convert temperatures to Kelvin by adding 273.15 to the Celsius value:

T₁ = 25.0°C + 273.15 = 298.15 K

Now, we can rearrange the equation to solve for the final temperature (T₂):

T₂ = (P₂ x T₁) / P₁

T₂ = (16212 millibars x 298.15 K) / 15198.75 millibars

T₂ = (4831940.8 millibars*K) / 15198.75 millibars

T₂ = 318.1 K

Finally, if you want the temperature back in Celsius:

T₂ = 318.1 K - 273.15 = 44.95°C

Thus, the final temperature of the gas would be approximately 44.95°C.