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laws

Question

The volume of a given mass of a gas at 27 $^{o} C$ , I atm is l00cc. What will be its volume at $327^{0} C$ ?

Easy

A

200 cc
B

150 cc
C

300 cc
D

100 cc

Solution

We have to convert the given temperatures in kelvin. If pressure of a given mass of the gas is kept constant then V $\propto$ T
$\Rightarrow \frac{V}{T} = constant [V = Volume of gas] [Temperature of gas]$
$\Rightarrow \frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}} \Rightarrow V_{2} = V_{1} (\frac{T_{2}}{T_{1}})$
Here we must convert the given temperature in kelvin.
$T_{1} = 273 + 27 = 300 K$
$T_{2} = 273 + 327 = 600 K$
But $V_{1} = 100 cc$
$V_{2} = V_{1} (\frac{600}{300}) \Rightarrow V_{2} = 2 V_{1}$
$∴ V_{2} = 2 \times 100 = 200 cc$

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