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  • If the pressure of an ideal gas in a closed container is increased by 2%, the temperature of the gas increases by<img alt="5^{\circ} \mathrm{C}" src="https://entrancecorner.oncodecogs.com/gif.latex

If the pressure of an ideal gas in a closed container is increased by 2%, the temperature of the gas increases by5^{\circ} \mathrm{C}. The initial temperature of the gas is

Option: 1

100 K


Option: 2

150 K


Option: 3

200 K


Option: 4

250 K


Answers (1)

best_answer

Since the volume of the gas is constant,

\mathrm{\frac{P_1}{P_2}=\frac{T_1}{T_2}}               ......[1]

\mathrm{\text { Now } P_2=P_1+0.02 P_1=1.02 P_1 \text { and } T_2=T_1+5}

Using these values in Eq. (1), we have

\mathrm{\frac{P_1}{1.02 P_1}=\frac{T_1}{T_1+5} \Rightarrow T_1=250 \mathrm{~K}}

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Sayak

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