Kinetic Theory - Result Question 4
4. At $10^{\circ} C$ the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$. At $110^{\circ} C$ this ratio is:
[2008]
(a) $x$
(b) $\frac{383}{283} x$
(c) $\frac{10}{110} x$
(d) $\frac{283}{383} x$
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Answer:
Correct Answer: 4. (d)
Solution:
- (d) Let the mass of the gas be $m$.
At a fixed temperature and pressure, volume is fixed.
Density of the gas, $\rho=\frac{m}{V}$
Now $\frac{\rho}{P}=\frac{m}{PV}=\frac{m}{nRT}$
$\Rightarrow \frac{m}{nRT}=x$ (By question)
$\Rightarrow xT=$ constant $\Rightarrow x_1 T_1=x_2 T_2$
$\Rightarrow x_2 \Rightarrow \frac{x_1 T_1}{T_2}=\frac{283}{383} x \begin{cases} \text{ Given } & \\ T_1 & =283 K \\ T_2 & =383 K \end{cases} $
