Question

At constant pressure, by what fraction of its volume will a quantity of gas change if the temperature changes from -173 degree Celsius to 27 degree Celsius?

Answer 1

Answer:-

Let the Volume of the gas be V and the Volume changed be x/y times of V.

Given:

Temperature of the gas (T1) = 27 ° .

Temperature changed (T2) = - 173°.

We know that,

Charle's Law of gases states that at constant pressure the Volume of given mass of a gas is directly proportional to its absolute temperature.

(Absolute temperature) = ° C + 273° K. (Approx.)

→ $V \: \alpha \: T$

(or)

V*T = K (Constant).

(or)

$\frac{V_{1} }{T _{1} } = \frac{V _{2} }{T _{2} } \\ \\ → \frac{V}{27 + 273} = \frac{ \frac{V \times x}{y}}{ - 173 + 273} \\ \\→ \frac{V}{300} = \frac{ \frac{V \times x}{y} }{100}$

After cross multiplication we get,

$100V = \frac{300 \times V\times x}{y} \\ \\ → \frac{x}{y} = \frac{100V}{300V} \\ \\ → \frac{x}{y} = \frac{1}{3}$

Hence, The Volume changes 1/3 times of itself when the temperature is changed from 27° to - 173°.