Answer:
i. The values for the graph are;
Volume Pressure
1 1
1/4 1
1 1/4
1 1
The graph is attached
ii. Energy is added to the system.
Explanation:
i) Here we note that Charles law states that the volume of a given mass of gas is directly proportional to its temperature at constant pressure.
Therefore;
T₁/V₁ = T₂/V₂
Where V₂ = V₁/4, we have;
T₁/V₁ = T₂/(V₁/4) = 4×T₂/V₁
T₁ = 4×T₂
Therefore, T₂ = T₁ /4
In process BC, whereby the gas expands isothermally to original volume, we have; according to Boyle's law
P₁·V₁ = P₂·V₂
V₁ = 4·V₂
∴ P₁·4·V₂ = P₂·V₂
4·P₁ = P₂
Process CA, gas returns to initial state with T₂ = T₁ /4
Therefore, we have from Pₐ·Vₐ/Tₐ = P₁·V₁/T₁
Where the volume remain constant, we have Gay Lussac's Law which states that the pressure of a given mass of gas is directly proportional to its temperature, therefore
P₁/T₁ = P₂/T₂
Hence; whereby the temperature changes from T₂ to T₁ and T₂ = T₁ /4, we have P₁ = 4·P₂
Therefore, the pressure increases by a factor of 4 × 4 = 16.
Please find the graph attached
ii) Given that the gas expands to its original volume V₁, such that V₁ = 4·V₂, also work done, W is given as follows;
[tex]W = nRTln\frac{v_f}{v_i} = nRTln\frac{v_1}{v_2} \ \because v_f =v_1 \ and \ v_i = v_2 \ also \ v_1 = 4\cdot v_2[/tex]
Therefore;
[tex]W = nRTln\frac{4\cdot v_2}{v_2} \ \therefore W = nRTln(4)[/tex]
Hence, as n, R, and T are all positive values, W is positive, energy is added to the system.
