The pressure of an ideal gas in a closed rigid vessel increases by 0.4% when its temperature is raised by 1°C. Its initial temperature is:
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Question

The pressure of an ideal gas in a closed rigid vessel increases by 0.4% when its temperature is raised by 1°C. Its initial temperature is:

G1 Physics · Accepted Answer

For a fixed amount of gas at constant volume, P/T = constant. Pressure increases by 0.4%, so P₂ = 1.004P₁. Temperature increases by 1 K: T₂ = T₁+1. Thus, P₂/P₁ = T₂/T₁. Therefore, 1.004 = (T₁+1)/T₁ = 1 + 1/T₁. Hence, 1/T₁ = 0.004 ⇒ T₁ = 250 K. Correct option: C.