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

final temperature T = 24.84ºC

Step-by-step 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)* Cv * (T-T1)_(cu) + M(oil) * Cv* (T-T2)_(oil)` = 0

put here value and we get T2

`8.94* 0.384 * (T-500) + 177.8 * 1.890* (T-20)` = 0

solve it we get

T = 24.84ºC