In a container of negligible heat capacity 100 gm of a liquid at 2 0 ∘ C is heated. Specific heat of the liquid varies with temperature given as s = ( 100 T + 500 ) J/kg ∘ C , where T is in ∘ C . Find

Question

In a container of negligible heat capacity 100 gm of a liquid at 2 0 ∘ C is heated. Specific heat of the liquid varies with temperature given as s = ( 100 T + 500 ) J/kg ∘ C , where T is in ∘ C . Find the amount of heat required to raise the temperature of the liquid to 4 0 ∘ C .

TestHub · Accepted Answer

Use the differential heat-capacity relation:
$d Q = m s d T$
$m = 0.1 kg$
$Q = \frac{100}{1000} \int_{20}^{40} (100 T + 500) d T$
$Q = 10 (\frac{T ^{2}}{2} + 5 T)_{20}^{40}$
$Q = 10 [\frac{4 0 ^{2} - 2 0 ^{2}}{2} + (40 - 20) 5]$
$Q = 10 [\frac{60 \times 20}{2} + 100]$
$Q = 10 \times 700 = 7000 J$

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