The initial temperature of a gas is $100^{\circ} C .$ The gas is contained in closed vessel. If the pressure of the gas is increased by $5 %,$ calculate the increase in temperature of the gas:

2^{\circ} C

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4^{\circ} C

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1^{\circ} C

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5^{\circ} C

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Solution

The correct option is D $5^{\circ} C$
We know that: $P V = R T$

Given: $P_{2} = P_{1} + 5 %$ of $P_{1}, V = c o n s t a n t$

Volume of gas is constant
By ideal gas equation we can say

$P \propto T$

$\frac{T_{1}}{T_{2}} = \frac{P_{1}}{P_{2}}$

Let $T_{2} = T_{1} + Δ T$

$\frac{100}{(100 + Δ T)} = \frac{P}{1.05 P}$

$105 P = 100 : P + P \times Δ T$

$\frac{5 P}{P} = Δ t = 5^{\circ} C$

$Final answer: (d)$

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