IIT-JEE 2010 · Paper 1 · Physics Q83

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PhysicsInteger+3Question 83 of 84

A piece of ice (heat capacity = 2100 J kg⁻¹ °C⁻¹ and latent heat = $3.36\times10^5$ J kg⁻¹) of mass m grams is at −5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is

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Answer and worked solution

Official answer: 8

Heat balance ( $m$ in grams):

warming the ice from −5 °C to 0 °C: $\dfrac m{1000}\times2100\times5=10.5m$ J;
melting 1 g: $\dfrac{3.36\times10^5}{1000}=336$ J.

$10.5m+336=420\implies m=8.$

Answer: 8

Topics:Latent heat and phase change Calorimetry and specific heat

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IIT-JEE 2010 · Paper 1, Physics question 83