An ice sample of mass m g initially at −5°C has specific heat 2100 J kg⁻¹ °C⁻¹ and latent heat of fusion 3.36×10⁵ J/kg. It receives 420 J, warming to 0°C and melting 1 g. Find m (g).
Physics · Mixed Chapter
JEE Main Practice

Question

An ice sample of mass m g initially at −5°C has specific heat 2100 J kg⁻¹ °C⁻¹ and latent heat of fusion 3.36×10⁵ J/kg. It receives 420 J, warming to 0°C and melting 1 g. Find m (g).

G1 Physics · Accepted Answer

Step 1: Heat used to melt 1 g at 0°C is Q_m=(0.001 kg)(3.36×10⁵ J/kg)=336 J. Step 2: Remaining heat to warm ice from −5°C to 0°C is 420−336=84 J. Step 3: Warming Q_w=(m/1000)×2100×5=10.5m J. Step 4: 10.5m=84 ⇒m=8 g.