Question

A uniform tube with piston in the middle and containing a gas at 0${}^0$C is heated to 100${}^0$C at one side . If the piston moves 5 cm, find the length of the tube containing the gas at 100${}^0$C.

• A. 16.75 cm
• B. 37.5 cm
• C. 28.25 cm
• D. 12.5 cm

Answer 1

Answer: (B)

37.5 cm

As $\frac{PV}{T}$ is constant for gas in both sections of the cylinder.

Let the length and area of the tube be $L$ and $A$, respectively.

For section with constant temperature,

$P_0{V}_0=P_1{V}_1$

$⟹P_{(}A\frac{L}{2})=P_1(A(\frac{L}{2}-5))$

Initial temperature $T_0=0^{o}C=273\text{K}$

Final temperature $T_1={100}^{o}C=100+273=373\text{K}$

Similarly for section whose temperature increased,

$\frac{P_0{V}_0}{T_0}=\frac{P_1{V}_1}{T_1}$
$⟹\frac{P_0\left(A\frac{L}{2}\right)}{273}=\frac{P_1\left(A\right(\frac{L}{2}+5\left)\right)}{373}$

$⟹L=65cm$

So the length of tube containing gas at ${100}^{\circ }$ is $\frac{L}{2}+5=37.5cm$