(a) Estimate the energy required to raise the temperature of a cup of coffee
from room temperature to $60 ^ { \circ } \mathrm { C }$ (b) Estimate the mass energy contained in a cup of hot
coffee.

Question

Quizplus · Accepted Answer

The Answer is (a) Assume a cup of hot coffee has a mass of 200 g and a room temperature of

20 ^ { \circ } \mathrm { C }

. Note the specific heat of coffee (mostly water) is

4186 \mathrm {~J} / \left( \mathrm { kg } \cdot { } ^ { \circ } \mathrm { C } ight)

. From equation (1.12) the thermal energy is given by

E = m c \Delta T = ( 0.2 \mathrm {~kg} ) imes \left( 4186 \mathrm {~J} / \left( \mathrm { kg } \cdot { } ^ { \circ } \mathrm { C } ight) ight) imes \left( 60 ^ { \circ } \mathrm { C } - 20 ^ { \circ } \mathrm { C } ight) = 3.35 imes 10 ^ { 4 } \mathrm {~J} ext {. }

(b) The mass energy is given by the Einstein's relation

E = m c ^ { 2 } = ( 0.2 \mathrm {~kg} ) imes \left( 3 imes 10 ^ { 8 } \mathrm {~m} / \mathrm { s } ight) ^ { 2 } = 1.8 imes 10 ^ { 16 } \mathrm {~J}

(A) Estimate the Energy Required to Raise the Temperature of a Cup