Out of the following,in which vessel will the temperature of the solution be higher after the salt is completely dissolved?

  • A
    $A$
  • B
    $B$
  • C
    Equal in both
  • D
    Information is not sufficient

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$A$ steel ball of mass $0.1 \, kg$ falls freely from a height of $10 \, m$ and bounces to a height of $5.4 \, m$ from the ground. If the dissipated energy in this process is absorbed by the ball,the rise in its temperature is ........... $^\circ C$ (Specific heat of steel $= 460 \, J \, kg^{-1} \, ^\circ C^{-1}, \; g = 10 \, m \, s^{-2}$)

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$A$ water cooler of storage capacity $120$ litres can cool water at a constant rate of $P$ watts. In a closed circulation system (as shown schematically in the figure),the water from the cooler is used to cool an external device that generates constantly $3 \text{ kW}$ of heat (thermal load). The temperature of water fed into the device cannot exceed $30^{\circ}\text{C}$ and the entire stored $120$ litres of water is initially cooled to $10^{\circ}\text{C}$. The entire system is thermally insulated. The minimum value of $P$ (in watts) for which the device can be operated for $3$ hours is (Specific heat of water is $4.2 \text{ kJ kg}^{-1} \text{K}^{-1}$ and the density of water is $1000 \text{ kg m}^{-3}$)

$A$ cube is subjected to a pressure $P$ on all its faces at a temperature of $0 \, ^\circ C$. By what temperature should the cube be heated so that it regains its original volume? Let the bulk modulus of the cube be $\beta$ and the coefficient of volume expansion be $\alpha$.

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