Question

An immersion heater is placed in crushed ice at –40°C, contained in a Perspex jar, such that water at 50°C is formed. If the power of the heater is 200 W and it is switched on for 3 min and 20 s, calculate the initial mass of ice. S.H.C. of ice = 2.1 Jg⁻¹°C⁻¹ and latent heat of ice = 336 Jg⁻¹.

Answer 1

Time = 3 min 20 s = 200 s

Q = Pt

= 200 × 200

= 40000 J

Let the initial mass of ice be m g.

Heat needed to warm ice from -40°C to 0°C:

Q₁ = m × 2.1 × 40

= 84 m J

Heat needed to melt ice at 0°C:

Q₂ = m × 336

= 336 m J

Heat needed to warm the water formed from 0°C to 50°C (taking the specific heat capacity of water as 4.2 J g⁻¹°C⁻¹):

Q₃ = m × 4.2 × 50

= 210 m J

Total heat needed (Q) = 84m + 336m + 210m = 630 m J

Equating heat supplied to heat needed:

630 m = 40000

$$m = \frac{40000}{630}$$

= 63.49 g

Therefore, the initial mass of ice is 63.49 g.