First slide

laws

Question

In order to increase the temperature of the gas filled in a closed vessel by 1^oC,its pressure is increased by 0.4%.The initial temperature of the gas is

Moderate

A

250^oC
B

250K
C

2500oC
D

25^oC

Solution

$T_{1}$ =T; $P_{1}$ =P;V=Constant
$T_{2}$ = $T_{1}$ + 1; $P_{2}$ = P+ $\frac{4 P}{1000;} μ = Constant$
We Know that
$Pv = μRT \frac{P_{1}}{P_{2}} = \frac{T_{1}}{T_{2}} \frac{P}{P + 4 P / 1000} = \frac{T}{T + 1} \frac{1}{1004^{} / 1000} = \frac{T}{T + 1} \frac{1000}{1004} = \frac{T}{T + 1} 1000 T + 1000 = 1004 T 1000 = 4 T \Rightarrow T = 250 K$

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