Question

1. A copper block of volume 1 L is heat treated at 500ºC and now cooled in a 200-L oil bath initially at 20◦C. Assuming no heat transfer with the surroundings, what is the final temperature?

Answer 1

Answer:

final temperature T = 24.84ºC

Explanation:

given data

copper volume = 1 L

temperature t1 = 500ºC

oil volume = 200 L

temperature t2 = 20ºC

solution

Density of copper $\rho$ cu = 8940 Kg/m³

Density of light oil  $\rho$ oil = 889 Kg/m³

Specific heat capacity of copper Cv = 0.384  KJ/Kg.K

Specific heat capacity of light oil Cv = 1.880 KJ/kg.K

so fist we get here mass of oil and copper that is

mass = density × volume   ................1

mass of copper = 8940 × 1 ×  $10^{-3}$  = 8.94 kg  

mass of oil = 889 × 200 × $10^{-3}$  =  177.8 kg  

so we apply here now energy balance equation that is

$M(cu)\times Cv \times (T-T1)_{cu} + M(oil) \times Cv\times (T-T2)_{oil}$  = 0

put here value and we get T2

$8.94\times 0.384 \times (T-500) + 177.8 \times 1.890\times (T-20)$  = 0

solve it we get

T = 24.84ºC