(D) The total energy stored in the spring is converted into heat energy when the vibrations stop due to damping.Energy stored in the spring $E = \frac

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(D) The total energy stored in the spring is converted into heat energy when the vibrations stop due to damping.Energy stored in the spring $E = \frac{1}{2} k x^2$.Given $k = 800\, N/m$ and $x = 2\, cm = 0.02\, m$.$E = \frac{1}{2} \times 800 \times (0.02)^2 = 400 \times 0.0004 = 0.16\, J$.This energy is absorbed by the mass and the water: $E = (m_1 s_1 + m_2 s_2) \Delta T$.Here $m_1 = 0.5\, kg$,$s_1 = 400\, J/kg\, K$,$m_2 = 1\, kg$,$s_2 = 4184\, J/kg\, K$.$0.16 = (0.5 \times 400 + 1 \times 4184) \Delta T$.$0.16 = (200 + 4184) \Delta T = 4384 \Delta T$.$\Delta T = \frac{0.16}{4384} \approx 3.65 \times 10^{-5}\, K$.The order of magnitude is $10^{-5}\, K$.

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Principle of Calorimetry and Water Equivalent

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$A$ massless spring $(k = 800\, N/m)$,attached with a mass $(500\, g)$ is completely immersed in $1\, kg$ of water. The spring is stretched by $2\, cm$ and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass $= 400\, J/kg\, K$,specific heat of water $= 4184\, J/kg\, K$)

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A
$10^{-3}\,K$
B
$10^{-4}\,K$
C
$10^{-1}\,K$
D
$10^{-5}\,K$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Principle of Calorimetry and Water Equivalent

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$A$ metal ball of mass $0.1 \, kg$ is heated up to $500 \, ^\circ C$ and dropped into a vessel of heat capacity $800 \, J K^{-1}$ containing $0.5 \, kg$ of water. The initial temperature of the water and the vessel is $30 \, ^\circ C$. The approximate percentage increment in the temperature of the water is ........ $\%$. [Specific heat capacities of water and metal are $4200 \, J kg^{-1} K^{-1}$ and $400 \, J kg^{-1} K^{-1}$ respectively.]

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$m$ g of water at $30^{\circ} C$ is mixed with $5$ g of ice at $-20^{\circ} C$. If the final equilibrium temperature of the mixture is $6^{\circ} C$,find the value of $m$. (Given: specific heat capacity of ice $= 0.5 \text{ cal g}^{-1} {}^{\circ} C^{-1}$,specific heat capacity of water $= 1 \text{ cal g}^{-1} {}^{\circ} C^{-1}$,and latent heat of fusion of ice $= 80 \text{ cal g}^{-1}$) (in $g$)

MediumAP EAMCET 2024

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The temperature of $100 \, g$ of water is to be raised from $24^{\circ} C$ to $90^{\circ} C$ by adding steam at $100^{\circ} C$ to it. The mass of the steam required for this purpose is ........... $g$.

$200 \, g$ of a solid ball at $20 \, ^oC$ is dropped into an equal amount of water at $80 \, ^oC$. The resulting temperature is $60 \, ^oC$. This means that the specific heat of the solid is

At a power station,heat is removed from the heat exchanger by cooling water at $6.7 \times 10^9 \ J$ per minute. The cooling water enters at $6.0 \ ^oC$ and leaves at $14.0 \ ^oC$. [Take the specific heat capacity of water $4200 \ J/kg \ ^oC$]. Which of the following is the rate of water flow?

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