A glass tube sealed at one end and containing a quantity of air is immersed in mercury until the sealed end is 10 cm from the surface of mercury in the vessel. At 0°C the level of mercury in the tube is 5 cm above the level of mercury in the vessel. The length of the tube is 15 cm. Temperature of the air in the tube will be raised by 221 × x kelvin so as to fill the tube completely. The atmospheric pressure is 75 cm of Hg. Neglect expansion of mercury and glass. Value of x is:
Physics · Mixed Chapter
JEE Mains

Question

A glass tube sealed at one end and containing a quantity of air is immersed in mercury until the sealed end is 10 cm from the surface of mercury in the vessel. At 0°C the level of mercury in the tube is 5 cm above the level of mercury in the vessel. The length of the tube is 15 cm. Temperature of the air in the tube will be raised by 221 × x kelvin so as to fill the tube completely. The atmospheric pressure is 75 cm of Hg. Neglect expansion of mercury and glass. Value of x is:

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Treat the trapped air as ideal gas and relate its initial and final states by P₁V₁/T₁=P₂V₂/T₂; the pressure is measured in the equivalent height of mercury. Step 2: At T₁=273 K, the trapped-air pressure differs from atmospheric pressure by the 5 cm Hg level difference; the final mercury level and the sealed-end depth determine the final gas volume. Step 3: Use the 15 cm tube length and 10 cm sealed-end immersion geometry to obtain the required temperature increase. Step 4: The source ke…