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Unit of Heat

Find the mass...

Question

Find the mass of the fuel required to raise the temperature of 2 kg of water in a copper container of mass 1 kg by 88^oC. Given calorific value of a fuel is 48 MJ kg^-1 , specific heat capacity of water is 1 cal g^-1^oC^-1 and specific heat capacity of copper is 0.095 cal g^-1^oC^-1

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Solution

$Hi, GIVEN : Mass of water = 2 Kg Mass of copper container = 1 kg Initial Temperature = 88 + 273 K = 361 K Final temperature (boiling point) = 373 K Calorific value of fuel = 48 MJ {Kg}^{- 1} Specific heat of water = 1 cal g^{- 1}^{°} C^{- 1} = 4.18 KJ / (KgK) Specific heat of copper container = 0.095 cal g^{- 1}^{°} C^{- 1} = 0.397 KJ / (KgK) Heat is required to raise the temperature of the water and also required to raise the temperature of copper container . Quantity of heat of heat required for the water Q_{w} = mc (t_{2} - t_{1}) = 2 \times 4.18 (373 - 361) = 100.32 K J Quantity of heat of heat required for the copper container Q_{c} = mc (t_{2} - t_{1}) = 1 \times 0.397 \times (373 - 361) = 4.764 K J Total quantity of heat required Q = Q_{w} + Q_{c} = 100.32 + 4.764 KJ = 105.084 KJ Regards$

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