Exams › JEE Main › Physics

A mercury thermometer has a bulb of volume V0 at 0 deg C and a capillary of cross-sectional area A0. The coefficient of linear expansion of glass is alpha_g per deg C and the coefficient of cubical (volume) expansion of mercury is gammaₘ per deg C. If mercury just fills the bulb at 0 deg C, find the length of the mercury column in the capillary at temperature T deg C.

1. V0*T*(gammaₘ + 3*alpha_g) / (A0*(1 + 2*alpha_g*T))
2. V0*T*(gammaₘ - 3*alpha_g) / (A0*(1 + 2*alpha_g*T))
3. V0*T*(gammaₘ + 2*alpha_g) / (A0*(1 + 3*alpha_g*T))
4. V0*T*(gammaₘ - 2*alpha_g) / (A0*(1 + 3*alpha_g*T))

Correct answer: V0*T*(gammaₘ - 3*alpha_g) / (A0*(1 + 2*alpha_g*T))

Solution

The mercury that overflows into the capillary equals V0*T*(gammaₘ - 3*alpha_g) (apparent expansion); dividing by the capillary area at T deg C, A0*(1 + 2*alpha_g*T), gives the column length.

Related JEE Main Physics questions

• A cube initially at 0°C is subjected to the same external pressure P on all its faces, causing it to be compressed. How much must its temperature be increased so that the cube regains its original size? The bulk modulus of the cube material is B and its coefficient of linear expansion is α.
• If λm represents the wavelength at which a black body emits radiation most strongly at temperature T K, then which relation is true?
• Which of the following statements about heat transfer is/are incorrect?
• A composite wall consists of two slabs, A and B, of equal thickness but made of different materials. Their thermal conductivities satisfy K_A = 3K_B. If the total temperature difference across the wall is 20°C, then in steady thermal equilibrium:
• An evacuated bulb contains a filament that is 10 cm long and 0.2 mm in diameter. If its emissivity is 0.2, determine the radiant power emitted by the filament at 2000 K. Take σ = 5.67 × 10⁻⁸ W/m² K⁴.
• A rectangular solid is raised in temperature from 0°C to 100°C. If its length increases by 0.10% over this interval, what is the corresponding percentage increase in its volume?

⚔️ Practice JEE Main Physics free + battle 1v1 →