Question

A metal block is made from a mixture of 2.4 kg of aluminum 1.6 kg brass and 0.8 kg of copper. The amount of heat required to raise the temperature of this block from 20 C to 80 C is (specific heats of aluminum, brass and copper are 0.216, 0.0917 and 0.0931 cal kg l ° C - respectively)

Answer 1

The amount of heat required to raise the temperature is 44.376  cal/°C

Explanation:

Mass of Al = 2.4 kg

Mass of brass = 1.6 kg

Mass of copper = 0.8 kg

Initial temperature = 20 °C

Final temperature = 80°C

Amount of heat required to raise the temperature = ?

Specific heat capacity of Al = 0.216 cal/ kg.°C

Specific heat capacity of brass = 0.216 cal/kg.°C

Specific heat capacity of Cu = 0.216 cal/kg°C

Solution:

Formula:

Q = m.c. ΔT

Q = amount of heat absorbed or released

m = mass of given substance

c = specific heat capacity of substance

ΔT = change in temperature

ΔT  = 80°C - 20°C = 60°C

Q = m₁ + m₂ + m₃

m₁ (Al)= m₁.c. ΔT

m₂( brass)= m₂c. ΔT

m₃(Cu) = m₃c. ΔT

m₁ (Al)= 2.4 kg×0.216 cal/kg.60°C

m₁ (Al) = 31.104 cal/°C

m₂( brass) = m₂c. ΔT

m₂( brass) = 1.6 kg×0.0917 cal/kg.60°C

m₂( brass) = 8.8032 cal/°C

m₃(Cu) = m₃c. ΔT

m₃(Cu) = 0.8 kg×0.0931 cal/kg.60°C

m₃(Cu) = 4.4688 cal/°C

Q = m₁ + m₂ + m₃

Q = 31.104 cal/°C + 8.8032 cal/°C + 4.4688 cal/°C

Q = 44.376  cal/°C