At a given temperature the pressure of a gas reduces to 75% of its initial value and the volume increases by 40% of its initial value. Find this temperature if the initial temperature was -10°C.
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Answer:
The final temperature is 3.15°C.
Explanation:
From the ideal gas equation,
P₁V₁ / T₁ = P₂V₂ / T₂
where,
P₁ = initial pressure P₂ = final pressure
V₁ = initial volume V₂ = final volume
T₁ = initial temperature T₂ = final temperature
Given that,
P₂ = 75% P₁ = 0.75 P₁
V₂ = V₁+40% V₁ = 140% V₁ = 1.4 V₁
T₁ = -10°C = -10+273 = 263K
substituting the values of T₁, P₂, and V₂ in the equation,
⇒ P₁V₁ / T₁ = 0.75P₁×1.4V₁ / T₂
⇒ 1 / 263 = 0.75×1.4 / T₂
⇒ T₂ = 0.75×1.4×263
⇒ = 276.15K = 3.15°C
Hence, the required answer is 3.15°C.
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