A closed hollow insulated cylinder is filled with gas at 0° C and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100° C. If the piston moves 5 cm the length of the hollow cylinder is

Question

A closed hollow insulated cylinder is filled with gas at 0° C and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100° C. If the piston moves 5 cm the length of the hollow cylinder is (A) 13.65 cm (B) 27.3 cm (C) 38.6 cm (D) 64.6 cm

Tardigrade Admin · Accepted Answer

Using Boyle's law, we have (V/T)= constant ⇒ ((l/2)+5/373)=((l/2)-5/273) As the piston moves 5 cm, the length of one side will be ((l/2)+5) and other side ((l/2)-5). On solving this equation, we get l=64.6 cm.

Q. A closed hollow insulated cylinder is filled with gas at 0∘C and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100∘C. If the piston moves 5cm the length of the hollow cylinder is

13.65 cm

27.3 cm

38.6 cm

64.6 cm

Using Boyle's law, we have TV​= constant ⇒3732l​+5​=2732l​−5​ As the piston moves 5cm, the length of one side will be (2l​+5) and other side (2l​−5). On solving this equation, we get l=64.6cm.

Using Boyle's law, we have $\frac{V}{T} =$ constant
$\Rightarrow \frac{\frac{l}{2} + 5}{373} = \frac{\frac{l}{2} - 5}{273}$
As the piston moves $5 c m$ , the length of one side will be
$(\frac{l}{2} + 5)$ and other side $(\frac{l}{2} - 5) .$
On solving this equation, we get $l = 64.6 c m$ .