Question

A gas occupies 24 liters at 458 K after it increase in pressure from 8 atm to 12 atm. Find the original temperature in degrees CELSIUS.

Answer 1

To find the initial temperature in degrees Celsius, we can use the combined gas law equation. This equation relates the initial and final states of the gas.

The combined gas law equation is:

(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)

Where:
P₁ is the initial pressure,
V₁ is the initial volume,
T₁ is the initial temperature,
P₂ is the final pressure,
V₂ is the final volume,
and T₂ is the final temperature.

Given information:
Initial pressure, P₁ = 8 atm
Final pressure, P₂ = 12 atm
Initial volume, V₁ = 24 liters
Final volume, V₂ = 24 liters (since the volume is not changing)
Final temperature, T₂ = 458 K

Now we can rearrange the equation to solve for the initial temperature, T₁:

(T₁) = (P₁ * V₁ * T₂) / (P₂ * V₂)

Plugging in the values:

T₁ = (8 atm * 24 L * 458 K) / (12 atm * 24 L)

Simplifying the equation:

T₁ = 1832 K

To convert the temperature to degrees Celsius, we need to subtract 273 from the Kelvin temperature:

T₁ = 1832 K - 273 K

T₁ = 1559 °C

Therefore, the original temperature in degrees Celsius is 1559 °C.