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 temper

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?

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Thanh Thu 4 years 2021-07-17T11:11:21+00:00 1 Answers 57 views 0

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  1. thucuc
    0
    2021-07-17T11:12:42+00:00
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    Answer:

    27°C

    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

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