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), tr e wat'r from the cooler is used to cool an external device that generates constantly $3 \mathrm{~kW}$ of heat (thermal load). The temperature of water fed into the device cannot exceed $30^{\circ} \mathrm{C}$ and the e.tire stored $120$ litres of water is initially cooled to $10^{\circ} \mathrm{C}$. The entire system is thermally insulat $\mathrm{d}$. The minimum value of $P$ (in watts) for which the device can be operated for $3$ hours is
(Specific heat of water is $4.2 \mathrm{~kJ}^{-1} \mathrm{~kg}^{-1}$ and the density of water is $10.$) $0 \mathrm{k}^2 \mathrm{~m}^{-3}$ )
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), tr e wat'r from the cooler is used to cool an external device that generates constantly $3 \mathrm{~kW}$ of heat (thermal load). The temperature of water fed into the device cannot exceed $30^{\circ} \mathrm{C}$ and the e.tire stored $120$ litres of water is initially cooled to $10^{\circ} \mathrm{C}$. The entire system is thermally insulat $\mathrm{d}$. The minimum value of $P$ (in watts) for which the device can be operated for $3$ hours is
(Specific heat of water is $4.2 \mathrm{~kJ}^{-1} \mathrm{~kg}^{-1}$ and the density of water is $10.$) $0 \mathrm{k}^2 \mathrm{~m}^{-3}$ )
- [IIT 2016]
- A
$1600$
- B
$2067$
- C
$2533$
- D
$3933$
Similar Questions
Due to cold weather a $1\, {m}$ water pipe of cross-sectional area $1\, {cm}^{2}$ is filled with ice at $-10^{\circ} {C}$. Resistive heating is used to melt the ice. Current of $0.5\, {A}$ is passed through $4\, {k} \Omega$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ? (In ${s}$)
(Given latent heat of fusion for water/ice $=3.33 \times 10^{5}\, {J} {kg}^{-1}$, specific heat of ice $=2 \times 10^{3}\, {J}$ ${kg}^{-1}$ and density of ice $=10^{3}\, {kg} / {m}^{3}$
Due to cold weather a $1\, {m}$ water pipe of cross-sectional area $1\, {cm}^{2}$ is filled with ice at $-10^{\circ} {C}$. Resistive heating is used to melt the ice. Current of $0.5\, {A}$ is passed through $4\, {k} \Omega$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ? (In ${s}$)
(Given latent heat of fusion for water/ice $=3.33 \times 10^{5}\, {J} {kg}^{-1}$, specific heat of ice $=2 \times 10^{3}\, {J}$ ${kg}^{-1}$ and density of ice $=10^{3}\, {kg} / {m}^{3}$
- [JEE MAIN 2021]
A $2\,kg$ copper block is heated to $500^o\,C$ and then it is placed on a large block of ice at $0^o\,C$. If the specific heat capacity of copper is $400\, J/kg/ ^o\,C$ and latent heat of fusion of water is $3.5 \times 10^5\, J/kg$, the amount of ice, that can melt is :-
A $2\,kg$ copper block is heated to $500^o\,C$ and then it is placed on a large block of ice at $0^o\,C$. If the specific heat capacity of copper is $400\, J/kg/ ^o\,C$ and latent heat of fusion of water is $3.5 \times 10^5\, J/kg$, the amount of ice, that can melt is :-
$1 \,kg$ of ice at $-20^{\circ} C$ is mixed with $2 \,kg$ of water at $90^{\circ} C$. Assuming that there is no loss of energy to the environment, the final temperature of the mixture is ............ $^{\circ} C$ (Assume, latent heat of ice $=334.4 \,kJ / kg$, specific heat of water and ice are $4.18 \,kJ kg ^{-1} K ^{-1}$ and $2.09 \,kJ kg ^{-1}- K ^{-1}$, respectively.)
$1 \,kg$ of ice at $-20^{\circ} C$ is mixed with $2 \,kg$ of water at $90^{\circ} C$. Assuming that there is no loss of energy to the environment, the final temperature of the mixture is ............ $^{\circ} C$ (Assume, latent heat of ice $=334.4 \,kJ / kg$, specific heat of water and ice are $4.18 \,kJ kg ^{-1} K ^{-1}$ and $2.09 \,kJ kg ^{-1}- K ^{-1}$, respectively.)
- [KVPY 2015]
An electric kettle (rated accurately at $2.5\, kW$) is used to heat $3\, kg$ of water from $15\,^oC$ to boiling point. It takes $9.5$ minute. Then, the amount of heat that has been lost is
An electric kettle (rated accurately at $2.5\, kW$) is used to heat $3\, kg$ of water from $15\,^oC$ to boiling point. It takes $9.5$ minute. Then, the amount of heat that has been lost is
A vessel contains $110\, g$ of water. The heat capacity of the vessel is equal to $10\, g$ of water. The initial temperature of water in vessel is $10°C.$ If $220\, g$ of hot water at $70°C$ is poured in the vessel, the final temperature neglecting radiation loss, will be........ $^oC$
A vessel contains $110\, g$ of water. The heat capacity of the vessel is equal to $10\, g$ of water. The initial temperature of water in vessel is $10°C.$ If $220\, g$ of hot water at $70°C$ is poured in the vessel, the final temperature neglecting radiation loss, will be........ $^oC$