How much heat energy is needed to raise the temperature of 2.66 kg of this oil from 23 °C to 191 °C?

Question

The specific heat of a certain type of cooking oil is 1.75 J/(g⋅°C). How much heat energy is needed to raise the temperature of 2.66 kg of this oil from 23 °C to 191 °C?

q= ?J

Answer 1

q = (ΔT)(c)(m)

plug in

ΔT = 191 – 23 = 168 °C

c = 1.75 J/(g⋅°C) = 1750 J/(kg⋅°C) [you need you mass units in c and m to match]

m = 2.66 kg

q = (168 °C)(1750 J/(kg⋅°C))(2.66 kg) = 782,040 J

(Not that even if you didn't know it, you could work out the formula by dimensional analysis.)

Answer (rounded to 3 significant figures)

q = 782,000 J (or 7.82 × 10⁵ J if scientific notation is required)

Answer 2

How much energy is needed to raise the temperature of 2.66 kg of cooking oil from 23 C⁰ to 191 C⁰?

The specific heat of a certain type of cooking oil is 1.75 J/(g⋅°C). How much heat energy is needed to raise the temperature of 2.66 kg of this oil from 23 °C to 191 °C?

SOLUTION

GIVEN DATA

mass (g) = m =2.66 kg = 2.66 g x 1000 g/kg = 2660 g

specific heat = c = 1.75 J/(g.C⁰)

ΔT = (191C⁰- 23 C⁰) = 168 C⁰

ΔH = m . c . ΔT

ΔH = 2660 g . 1.75 J/(g.C⁰) .168 C⁰ = 782040 J = 782.040 KJ

ΔH = 782040 J = 7.82 x 10⁵ J