Principle of Calorimetry and Water Equivalent PYQs: JEE Mains Physics

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1. 1. 10 kg of ice at \(-10^{\circ}C\) is added to 100 kg of water to lower its temperature from \(25^{\circ}C.\) Consider no heat exchange to surroundings. The decrement to the temperature of water is ___________ \(^{\circ}C.\)
   (specific heat of ice \(= 2100\ J/Kg.^{\circ}C\), specific heat of water \(= 4200\ J/Kg.^{\circ}C\), latent heat of fusion of ice \(= 3.36 \times 10^{5}\ J/Kg\)) 2026 Hard
2. 2. A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is __________ grams.
   (Latent heat of fusion of lead \(=2.5 \times 10^4 \mathrm{JKg}^{-1}\) and specific heat capacity of lead \(=125 \mathrm{JKg}^{-1}\) \(\left.\mathrm{K}^{-1}\right)\) 2025 Medium
3. 3. A water heater of power \(2000\,W\) is used to heat water. The specific heat capacity of water is \(4200\,J\,kg ^{-1}\, K ^{-1}\). The efficiency of heater is \(70 \%\). Time required to heat \(2\,kg\) of water from \(10^{\circ}\,C\) to \(60^{\circ}\,C\) is \(..........s\). (Assume that the specific heat capacity of water remains constant over the temperature range of the water). 2023 Medium
4. 4. Heat energy of \(184\,kJ\) is given to ice of mass \(600\,g\) at \(-12^{\circ}\,C\), Specific heat of ice is \(2222.3\,J\,kg ^{-1^{\circ}}\,C ^{-1}\) and latent heat of ice in \(336\,kJ / kg ^{-1}\) \((A)\) Final temperature of system will be \(0^{\circ} C\). \((B)\) Final temperature of the system will be greater than \(0^{\circ} C\). \((C)\) The final system will have a mixture of ice and water in the ratio of \(5: 1\). \((D)\) The final system will have a mixture of ice and water in the ratio of \(1: 5\). \((E)\) The final system will have water only. Choose the correct answer from the options given below: 2023 Hard
5. 5. A \(100 \,g\) of iron nail is hit by a \(1.5\, kg\) hammer striking at a velocity of \(60\, ms ^{-1}\). \(............^{\circ}C\) will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail . [Specific heat capacity of iron  \(=0.42\, Jg ^{-1}{ }\,^{\circ}C ^{-1}\) ] 2022 Medium
6. 6. A block of ice of mass \(120\,g\) at temperature \(0^{\circ} C\) is put in \(300\,gm\) of water at \(25^{\circ} C\). The \(xg\) of ice melts as the temperature of the water reaches \(0^{\circ} C\). The value of \(x\) is [Use: Specific heat capacity of water \(=4200\) \(J\,kg ^{-1} K ^{-1}\), Latent heat of ice \(\left.=3.5 \times 10^{5} J\,kg ^{-1}\right]\) 2022 Medium
7. 7. A copper block of mass \(5.0\, kg\) is heated to a temperature of \(500^{\circ} C\) and is placed on a large ice block. What is the maximum amount of ice (ઇન \(kg\)) that can melt? [Specific heat of copper: \(0.39\, Jg ^{-1 \circ} C ^{-1}\) and latent heat of fusion of water : \(335 \,J g ^{-1}\) ] 2022 Medium
8. 8. A geyser heats water flowing at a rate of \(2.0 kg\) per minute from \(30^{\circ} C\) to \(70^{\circ} C\). If geyser operates on a gas burner, the rate of combustion of fuel will be \(\dots \; g \min ^{-1}\) [Heat of combustion \(=8 \times 10^{3} Jg ^{-1}\)  Specific heat of water \(=4.2 Jg ^{-1} \; { }^{\circ} C ^{-1}\) ] 2022 Hard
9. 9. A lead bullet penetrates into a solid object and melts. Assuming that \(40 \%\) of its kinetic energy is used to heat it, the initial speed of bullet is ............ \(ms ^{-1}\) (Given, initial temperature of the bullet \(=127^{\circ} C\), Melting point of the bullet \(=327^{\circ} C\), Latent heat of fusion of lead \(=2.5 \times 10^{4} \,J Kg ^{-1}\), Specific heat capacity of lead \(=125 \,J / kg K\) ) 2022 Medium
10. 10. A steam engine intakes \(50\, g\) of steam at \(100^{\circ} C\) per minute and cools it down to \(20^{\circ} C\). If latent heat of vaporization of steam is \(540 \,cal g ^{-1}\), then the heat rejected by the steam engine per minute is .........\(\times 10^{3}\)\(cal.\) 2022 Medium
11. 11. 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 \(=10^{3}\, {kg} / {m}^{3}\) 2021 Hard
12. 12. The temperature of equal masses of three different liquids \({x}, {y}\) and \({z}\) are \(10^{\circ} {C}, 20^{\circ} {C}\) and \(30^{\circ} {C}\) respectively. The temperature of mixture when \({x}\) is mixed with \({y}\) is \(16^{\circ} {C}\) and that when \({y}\) is mixed with \(z\) is \(26^{\circ} {C}\). The temperature of mixture when \(x\) and \(z\) are mixed will be ...... \(^{\circ} {C}\) 2021 Hard
13. 13. A calorimeter of water equivalent \(20\, g\) contains \(180\, g\) of water at \(25^{\circ} C\). '\(m\)' grams of steam at \(100^{\circ} C\) is mixed in it till the temperature of the mixure is \(31^{\circ} C\). The value of \('m'\) is close to (Latent heat of water \(=540\) cal \(g ^{-1}\), specific heat of water \(=1\) cal \(g^{-1}{ }^{\circ} C ^{-1}\) ) 2020 Medium
14. 14. \(M\) grams of steam at \(100^{\circ} \mathrm{C}\) is mixed with \(200\; \mathrm{g}\) of ice at its melting point in a thermally insulated container. If it produces liquid water at \(40^{\circ} \mathrm{C}\) [heat of vaporization of water is \(540 \;cal/\mathrm{g}\) and heat of fusion of ice is \(80 \;\text { cal/g }]\) the value of \(\mathrm{M}\) is 2020 Medium
15. 15. The specific heat of water \(=4200\, J\, kg ^{-1}\, K ^{-1}\) and the latent heat of ice \(=3.4 \times 10^{5}\, J\, kg ^{-1}.\) \(100\) grams of ice at \(0^{\circ} C\) is placed in \(200\, g\) of water at \(25^{\circ} C\). The amount of ice that will melt as the temperature of water reaches \(0^{\circ} C\) is close to (in \(grams\))  2020 Medium
16. 16. A metal bal of mass \(0.1\, kg\) is heated upto \(500\,{}^oC\) and dropped into a vessel of heat capacity \(800\, JK^{-1}\) and containing \(0.5\, kg\) water. The initial temperature of water and vessel is \(30\,{}^oC\). ........ \(\%\) is the approximate percentage increment in the temperature of the water. [Specific heat Capacities of water and metal are, respectively \(4200\, Jkg^{-1}K^{-1}\) and \(400\, Jkg^{-1}K^{-1}\)] 2019 Hard
17. 17. An unknown metal of mass \(192\, g\) heated to a temperature of \(100\,^oC\) was immersed into a brass calorimeter of mass \(128\, g\) containing \(240\, g\) of water at a temperature of \(8.4\,^oC\). Calculate the specific heat of the unknown metal if water temperature stabilizes at \(21.5\,^oC\). (Specific heat of brass is \(394\, J\, kg^{-1}\, K^{-1}\)) ......... \(J\, kg^{-1}\, K^{-1}\) 2019 Medium
18. 18. Ice at \(-20\,^oC\) is added to \(50\,g\) of water at \(40\,^oC.\) When the temperature of the mixture reaches \(0\,^oC,\) it is found that \(20\,g\) of ice is still unmelted. The amount of ice added to the water was close to ........\(g\) (Specific heat of water \(= 4.2\,J/g/^oC)\) Heat of fusion of water at \(0^oC = 334\,J/g\) ) 2019 Medium
19. 19. When \(100\,g\) of a liquid \(A\) at \(100\,^oC\) is added to \(50\,g\) of a liquid \(B\) at temperature \(75\,^oC\), the temperature of the mixture becomes \(90\,^oC\). The temperature of the mixture, if \(100\,g\) of liquid \(A\) at \(100\,^oC\) is added to \(50\,g\) of liquid \(B\) at \(50\,^oC\), will be ........\(^oC\) 2019 Hard
20. 20. A copper ball of mass \(100\ gm\) is at a temperature \(T\). It is dropped in a copper calorimeter of mass \(100\ gm\), filled with \(170\  gm\) of water at room temperature. Subsequently, the temperature of the system is found to be \(75^o C\). \(T\) is given by......\(^oC\) (Given : room temperature \(= 30^o  C\), specific heat of copper \(=\) \(0.1\) \(cal/gm^o C\)) 2017 Medium
21. 21. In an experiment a sphere of aluminium of mass \(0.20\, kg\) is heated upto \(150\,^oC\). Immediately, it is put into water of volume \(150\, cc\) at \(27\,^oC\) kept in a calorimeter of water equivalent to \(0.025\, kg\). Final temperature of the system is \(40\,^oC\). The specific heat of aluminium is ............ \(J/kg\,-\,^oC\) (take \(4.2\, Joule= 1\, calorie\)) 2017 Hard
22. 22. An experiment takes \(10\, minutes\) to raise the temperature of water in a container from \(0\,^oC\) to \(100\,^oC\) and another \(55\, minutes\) to convert it totally into steam by a heater supplying heat at a uniform rate . Neglecting the specific heat of the container and taking specific heat of water to be \(1\, cal / g\,^oC\), the heat of vapourization according to this experiment will come out to be ........ \(cal/g\) 2015 Medium
23. 23. Water of volume \(2\, L\) in a closed container is heated with a coil of \(1\,kW\). While water is heated, the container loses energy at a rate of \(160\, J/s\) . In how much time will the temperature of water rise from \(27\,^oC\) to \(77\,^oC\) ? (Specific heat of water is \(4.2\, kJ/kg\) and that of the container is negligible) 2014 Hard
24. 24. \(500\, g\) of water and \(100\, g\) of ice at \(0\,^oC\) are in a calorimeter whose water equivalent is \(40\, g\). \(10\, g\) of steam at \(100\,^oC\) is added to it. Then water in the calorimeter is ....... \(g\) (Latent heat of ice \(\,= 80\, cal/g\), Latent heat of steam \(\,= 540\, cal/ g\)) 2013 Medium
25. 25. A mass of \(50\,g\) of water in a closed vessel, with surroundings at a constant temperature takes \(2\, minutes\) to cool from \(30\,^oC\) to \(25\,^oC\). A mass of \(100\,g\) of another liquid in an identical vessel with identical surroundings takes the same time to cool from \(30\,^oC\) to \(25\,^o C\). The specific heat of the liquid is .......... \(kcal/kg\) (The water equivalent of the vessel is \(30\,g\).) 2013 Hard

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