Q.1 (ix) If pressure of gas contained in a closed vessel is increased by 0.4% when heated by 1°C, its initial temperature must be _____.
A. 200°C
B. 250°C
C. 300°C
D. 350°C
Best answer
Answer: B. 250°C
Answer: (b) 250 (the value is 250 K, not 250°C)
At constant volume \(P \propto T\) (absolute temperature), so \(\dfrac{\Delta P}{P} = \dfrac{\Delta T}{T}\). A rise of 1°C is a rise of 1 K.
\[\frac{0.4}{100} = \frac{1}{T} \Rightarrow T = \frac{100}{0.4} = 250\ \text{K}\]So the initial temperature is 250 K \(= 250 - 273 = -23\)°C. The options are printed in °C, so none is literally correct; the intended answer is option (b), 250, read as 250 K.
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