Question

A gas occupies 2 m^3 at 27°C at a pressure of 1 atmosphere. At a pressure of 2 atmospheres it occupies a volume of 1 m^2. What is its temperature at this new volume and pressure?

Answer 1

27°C

Step-by-step explanation:

We'll begin by converting 27 °C to Kelvin temperature. This can be obtained as follow:

T(K) = T(°C) + 273

Initial temperature (T₁) = 27 °C

Initial temperature (T₁) = 27 °C + 273

Initial temperature (T₁) = 300 K

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

Initial volume (V₁) = 2 m³

Initial temperature (T₁) = 300 K

Initial pressure (P₁) = 1 atm

Final pressure (P₂) = 2 atm

Final volume (V₂) = 1 m³

Final temperature (T₂) =?

P₁V₁/T₁ = P₂V₂/T₂

1 × 2 / 300 = 2 × 1 / T₂

2/300 = 2/T₂

1/150 = 2/T₂

Cross multiply

T₂ = 150 × 2

T₂ = 300 K

Finally, we shall convert 300 K to celsius temperature. This can be obtained as follow:

T(°C) = T(K) – 273

T(K) = 300 K

T(°C) = 300 – 273

T(°C) = 27°C

Thus, the final temperature is 27°C