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question_answer1) Temperature difference of \[120{}^\circ C\] is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length\[\frac{3L}{2}\], is connected across AB (See figure). In steady state, temperature difference (in\[{}^\circ C\]) between P and Q will be close to:
question_answer2) A heat source at \[T={{10}^{3}}K\] is connected to another heat reservoir at \[T={{10}^{2}}K\] by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is \[0.1W{{K}^{-1}}{{m}^{-1}}\] , the energy flux (in \[W/{{m}^{2}}\]) through it in the steady state is:
question_answer3) An unknown metal of mass 192 g heated to a temperature of \[100{}^\circ C\] was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of \[8.4{}^\circ C\]. Calculate the specific heat (in \[J\,\,k{{g}^{-1}}{{K}^{-1}}\]) of the unknown metal if water temperature stabilizes at \[21.5{}^\circ C\]. (Specific heat of brass is 394 \[J\,\,k{{g}^{-1}}{{K}^{-1}}\])
question_answer4) 2 kg of a monoatomic gas is at a pressure of \[4\times {{10}^{4}}\,\,N/{{m}^{2}}\]. The density of the gas is \[8\,\,kg/{{m}^{3}}\]. What is the energy (in joule) of the gas due to its thermal motion?
question_answer5) Ice at \[-20{}^\circ C\] is added to 50 g of water at \[40{}^\circ C\]. When the temperature of the mixture reaches \[0{}^\circ C\], it is found that 20 g of ice is still unmelted. The amount (in gram) of ice added to the water was (Specific heat of water \[=4.2J/g/{}^\circ C\] Specific heat of Ice \[=2.1\text{ }J/g/{}^\circ C\] Heat of fusion of water at \[0{}^\circ C=334J/g\]
question_answer6) Two rods A and B of identical dimensions are at temperature\[30{}^\circ C\]. If A is heated up to \[180{}^\circ C\]and B up to\[T{}^\circ C\], then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4:3, then the value of T (in\[{}^\circ C\]) is:
question_answer7) When 100g of a liquid A at \[100{}^\circ C\] is added to 50 g of a liquid B at temperature \[75{}^\circ C\], the temperature of the mixture becomes \[90{}^\circ C\]. The temperature of the mixture (in \[{}^\circ C\]), if 100g of liquid A at \[100{}^\circ C\] is added to 50 g of liquid B at \[50{}^\circ C\], will be:
question_answer8) A thermometer graduated according to a linear scale reads a value \[{{x}_{0}}\] when in contact with boiling water, and \[{{x}_{0}}/3\] when in contact with ice. What is the temperature of an object in \[{}^\circ C\], if this thermometer in the contact with the object reads \[{{x}_{0}}/2?\]
question_answer9) A thermally insulted vessel contains 150 g of water at\[0{}^\circ C\]. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at \[0{}^\circ C\] itself. The mass (in gram) of evaporated water will be close to : (Latent heat of vaporization of water\[=2.10\times {{10}^{6\,}}\,J\,k{{g}^{-1}}\]and Latent heat of fusion of water\[=3.36\times {{10}^{5\,}}\,J\,k{{g}^{-1}})\]
question_answer10) A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat (in joule) needed to raise the temperature of the gas by \[20{}^\circ C\] is : [Given that\[R=8.31\text{ }J\,mo{{l}^{-1}}\,\,{{K}^{-1}}\]]
question_answer11) The coefficient of cubical expansion of mercury is \[0.00018\text{ }/{}^\circ C\] and that of brass \[0.00006/{}^\circ C\]. If a barometer having a brass-scale were to read 74.5 cm at \[30{}^\circ C\], find the true barometric height (in cm) at \[0{}^\circ C\]. The scale is supposed to be correct at \[15{}^\circ C\].
question_answer12) A bar with a crack at its centre buckles as a result of temperature rise of\[32\text{ }{}^\circ C\]. If the fixed distance \[{{L}_{0}}\] is 3.77 m and the coefficient of linear expansion of the bar is \[25\text{ }\times \,\,\text{1}{{\text{0}}^{-6}}/{}^\circ C\] find the rise (in metre) of the centre.
question_answer13) In an experiment on the specific heat of a metal a 0.20 kg block of the metal at \[150\text{ }{}^\circ C\] is dropped in a copper calorimeter (of water equivalent 0.025 kg) containing \[150\text{ c}{{\text{m}}^{3}}\] of water at \[27\text{ }{}^\circ C\]. The final temperature is \[40\text{ }{}^\circ C\]. Compute the specific heat (in \[J\,\,k{{g}^{-1}}\,\,{}^\circ {{C}^{-1}}\]) of the metal.
question_answer14) The temperature of equal masses of three different liquids A, B and C are \[12\text{ }{}^\circ C\], \[19\text{ }{}^\circ C\] and \[28{}^\circ C\] respectively The temperature when A and B are mixed is \[16\text{ }{}^\circ C\] and when B and C are mixed it is \[23\text{ }{}^\circ C\]. What should be the temperature (in \[{}^\circ C\]) when A and C are mixed?
question_answer15) A body initially at \[80{}^\circ C\] cools to \[64{}^\circ C\] in 5 minutes and to \[52{}^\circ C\] in 10 minutes. What will be the temperature (in \[{}^\circ C\]) after 15 minutes?
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