Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by 1°C. Its initial temperature must be: [2025]

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Solution

Q.
Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by 1°C. Its initial temperature must be: [2025]

1 25°C

2 2500 K

3 250 K

4 250°C

Ans.
(3)

Isochoric process, P $\propto$ T

$\frac{P}{T} = constant \Rightarrow \frac{△ P}{P} = \frac{△ T}{T}$

$\frac{0.4}{100} = \frac{1}{T} \Rightarrow T = \frac{100}{0.4} = 250 K$

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