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Question

Pressure remaining the same, the volume of a given mass of an ideal gas increases for every degree centigrade rise in temperature by definite fraction of its volume at:

A
Its Boyle temperature
B
$$0^{o} C$$
C
Its critical temperature
D
Absolute zero
Solution
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Correct option is A. $$0^{o} C$$
$$V_{t} = V_{o}\ (1+\alpha_{v} t)$$

$$\because (V_{2} - V_{1}) = \Delta V = V_{0} \alpha (t_{2} - t_{1})$$

if $$t_{2} - t_{1} = 1^{o}$$ then $$\Delta V = \alpha V_{o}$$

For every $$1^{o}C$$ increase in temperature, the volume of a given mass of an ideal gas increases by a definite fraction $$ \dfrac{1}{273.15}$$ of $$V_{o}$$.

Here $$V_{o}$$ is volume at $$0^{o}C$$ temperature.

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