Question

Sulphur dioxide (S02) is circulated as the refrigerant in a small refrigerator. S02 gas pressure of 5 bar and Temperature 340k is to be cooled at constant volume of o. 142 meter cube to 293k as part of the refrigeration cycle. Calculate ay The heat liberated by The work done by the gas on cooling, The final pressure attained on cooling and dy The change in enthalpy Sulphur dioxide may be treated as an ideal gas The specific heart (J/mol.k) is found to vary with temperature k according to
Cp = 25.736 +5.796410 27 – 3.8112 x 15872 + 8.612 x 10 9 T3 T = 340k To=293k ​

Answer 1

Answer:

$Prove that the general solution of sin θ = sin ∝ is given by θ = nπ + (-1)[Math Processing Error]n ∝, n ∈ Z.</p><p></p><p>Solution:</p><p></p><p>We have,</p><p></p><p>sin θ = sin ∝            </p><p></p><p>⇒ sin θ - sin ∝ = 0 </p><p></p><p>⇒ 2 cos [Math Processing Error]θ+∝2 sin[Math Processing Error]θ−∝2 = 0</p><p></p><p>Therefore either cos [Math Processing Error]θ+∝2 = 0 or, sin [Math Processing Error]θ−∝2 = 0</p><p></p><p>Now, from cos [Math Processing Error]θ+∝2 = 0 we get, [Math Processing Error]θ+∝2 = (2m + 1)[Math Processing Error]π2, m ∈ Z</p><p></p><p>⇒ θ = (2m + 1)π - ∝, m ∈ Z i.e., (any odd multiple of π) - ∝ ……………….(i)</p><p></p><p>And from sin [Math Processing Error]θ−∝2= 0 we get,</p><p></p><p>[Math Processing Error]θ−∝2 = mπ, m ∈ Z                  </p><p></p><p>⇒ θ = 2mπ + ∝, m ∈ Z i.e., (any even multiple of π) + ∝ …………………….(ii)</p><p></p><p>Now combining the solutions (i) and (ii) we get,</p><p></p><p>θ = nπ + (-1)[Math Processing Error]n∝, where n ∈ Z.</p><p></p><p>Hence, the general solution of sin θ = sin ∝ is θ = nπ + (-1)[Math Processing Error]n ∝, where n ∈ Z.</p><p></p><p>Note: The equation csc θ = csc ∝ is equivalent to sin θ = sin ∝ (since, csc θ = [Math Processing Error]1sinθ and csc ∝ =[Math Processing Error]1sin∝). Thus, csc θ = csc ∝ and sin θ = sin ∝ have the same general solution.</p><p></p><p>Hence, the general solution of csc θ = csc ∝ is θ = nπ + (-1)[Math Processing Error]n ∝, where n ∈ Z.</p><p></p><p>$