A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8 kg. Find the rise in temperature of the block in 2.5 minutes, assuming 50 % power is used up in heating the machine itself or lost to the surroundings. (Specific heat of aluminium = 0.91 J g-1 °C-1)

Question

A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8 kg. Find the rise in temperature of the block in 2.5 minutes, assuming 50 % power is used up in heating the machine itself or lost to the surroundings. (Specific heat of aluminium = 0.91 J g-1 °C-1) (A) 100 °C (B) 103 °C (C) 150 °C (D) 155 °C

Tardigrade Admin · Accepted Answer

Here, P = 10 kW = 104 W, m = 8 kg time, t = 2.5 minute = 2.5 × 60 = 150 s Specific heat, s = 0.91 J g-1 C-1 Total energy = P × t = 104 × 150 = 15 × 105 J As 50 % of energy is lost, ∴ Energy available, Δ Q=(1/2)×15×105=7.5 ×105 J As Δ Q=msΔ T Δ T=(Δ Q/ms)=(7.5 × 105/8 × 103 × 0.91)≈103 °C

$100^{\circ} C$

$103^{\circ} C$

$150^{\circ} C$

$155^{\circ} C$

Q. A 10kW drilling machine is used to drill a bore in a small aluminium block of mass 8kg. Find the rise in temperature of the block in 2.5 minutes, assuming 50% power is used up in heating the machine itself or lost to the surroundings. (Specific heat of aluminium =0.91Jg−1∘C−1)

100∘C

103∘C

150∘C

155∘C

Here, P=10kW=104W, m=8kg time, t=2.5minute=2.5×60=150s Specific heat, s=0.91Jg−1C−1 Total energy =P×t=104×150=15×105J As 50% of energy is lost, ∴ Energy available, ΔQ=21​×15×105=7.5×105J As ΔQ=msΔT ΔT=msΔQ​=8×103×0.917.5×105​≈103∘C

$100^{\circ} C$

$103^{\circ} C$

$150^{\circ} C$

$155^{\circ} C$