Question

4. Hot exhaust gases are often used in a chemical plant to heat chemical reactions before the

gases are discharged to the atmosphere. If 10.0 L of gas at 300°C and 3.00 atm expand to
125 L at 1.00 atm during the heat exchange process, what is the temperature of the gas
that is released to the atmosphere?

Answer 1

1,250 °C

Step-by-step explanation:

To find the new temperature, you need to use a variation of the Combined Gas Law. The equation looks like this:

P₁V₁ / T₁ = P₂V₂ / T₂

In this formula, "P₁", "V₁" and "T₁" represent the initial pressure, volume, and temperature. "P₂", "V₂", and "T₂" represent the final pressure, volume, and temperature. You can find the new temperature by plugging the given values into the equation and simplifying.

P₁ = 3.00 atm P₂ = 1.00 atm

V₁ = 10.0 L V₂ = 125 L

T₁ = 300 °C T₂ = ? °C

P₁V₁ / T₁ = P₂V₂ / T₂ <----- Combined Law equation

(3.00 atm)(10.0 L) / (300 °C) = (1.00 atm)(125 L) / T₂ <----- Insert values

0.1 = (1.00 atm)(125 L) / T₂ <----- Simplify left side

0.1 = 125 / T₂ <----- Multiply 1.00 and 125

0.1 x T₂ = 125 <----- Multiply both sides by T₂

T₂ = 1,250 <----- Divide both sides by 0.1