A thin-walled cylindrical metal vessel with a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The coefficient of volume expansion of the vessel is $\gamma_{	ext{vessel}} = 3 \alpha_{	ext{vessel}} = 3 	imes 10^{-3} \ ^\circ C^{-1}$.The co

Vedclass · Accepted Answer

decreases by $2\%$

Vedclass · Answer

(C) The coefficient of volume expansion of the vessel is $\gamma_{	ext{vessel}} = 3 \alpha_{	ext{vessel}} = 3 	imes 10^{-3} \ ^\circ C^{-1}$.The coefficient of volume expansion of the liquid is $\gamma_{	ext{liquid}} = 10^{-3} \ ^\circ C^{-1}$.Since $\gamma_{	ext{vessel}} > \gamma_{	ext{liquid}}$,the volume of the vessel increases more than the volume of the liquid upon heating. This causes the liquid level to fall,resulting in a decrease in pressure at the bottom.The change in volume of the vessel relative to the liquid is given by $\Delta V_{	ext{rel}} = V(\gamma_{	ext{vessel}} - \gamma_{	ext{liquid}}) \Delta T$.Substituting the values: $\Delta V_{	ext{rel}} = V(3 	imes 10^{-3} - 1 	imes 10^{-3}) 	imes 10 = V(2 	imes 10^{-3}) 	imes 10 = 0.02 V$.Since the cross-sectional area $A$ of the cylinder also increases,the change in height $\Delta h$ is related to the change in volume. For a thin-walled vessel,the fractional change in height is $\frac{\Delta h}{h} \approx \frac{\Delta V}{V} = 0.02$.Pressure $P = h ho g$. The fractional change in pressure is $\frac{\Delta P}{P} = \frac{\Delta h}{h} = 0.02$.Therefore,the pressure decreases by $0.02 	imes 100\% = 2\%$.

$A$ thin-walled cylindrical metal vessel with a linear coefficient of expansion $10^{-3} \ ^\circ C^{-1}$ contains benzene with a volume expansion coefficient of $10^{-3} \ ^\circ C^{-1}$. If the vessel and its contents are heated by $10 \ ^\circ C$,the pressure due to the liquid at the bottom:

Similar Questions

$2 \ kg$ of ice at $-20^{\circ} C$ is mixed with $5 \ kg$ of water at $20^{\circ} C$. What is the final amount of water in the mixture (in $kg$)? (Given: specific heat of ice $= 0.5 \ cal/g^{\circ} C$,specific heat of water $= 1 \ cal/g^{\circ} C$,latent heat of fusion of ice $= 80 \ cal/g$)

$A$ lead bullet moving with velocity $V$ strikes a wall and stops. If $75 \%$ of its energy is converted into heat,then the increase in temperature is ($s=$ specific heat of lead,$J=$ mechanical equivalent of heat).

$A$ lead bullet moving with velocity '$v$' strikes a wall and stops. If $50\%$ of its energy is converted into heat,then the increase in temperature is ($s =$ specific heat of lead,$J =$ mechanical equivalent of heat).

How much energy will be released by cooling $1\,kg$ of water up to a temperature of $10\,^{\circ}C$?

The height of a waterfall is $50 \ m$. If $g = 9.8 \ m/s^2$, the difference between the temperature at the top and the bottom of the waterfall is: (in $^{\circ} C$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module