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Question 12

For three low density gases $$A, B, C$$ pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point '$$K$$' is:

image

Solution

For a gas at constant volume,

$$PV=nRT$$

so

$$P=\frac{nR}{V}T$$

This shows pressure is directly proportional to absolute temperature (Kelvin), not Celsius.

If temperature is written in Celsius (t), then

$$T=t+273$$

So

$$P=\frac{nR}{V}(t+273)$$

When pressure becomes zero,

$$t=-273^{\circ}C$$

This is absolute zero.

All straight lines extrapolate to meet the temperature axis at this same point K.

Therefore point K corresponds to

$$-273^{\circ}C$$

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