An insulated Thermos contains a volume V of hot coffee at temperature T . You pu

Question

An insulated Thermos contains a volume V of hot coffee at temperature T. You put in an ice cube with mass m at its melting point to cool the coffee. What is the temperature of the contents of your Thermos once the ice cube has melted? Treat the coffee as though it were pure water and neglected energy exchanges with the environment. (Use any variable or symbol stated above along with the following as necessary: c for the specific heat of water, Lf for the latent heat of fusion of water, and for the density of water.)
Tf =

Explanation / Answer

Since ise cube has melted, temperature will be somewhere between 0 and T.
Let this temperature be Tf.

mass of coffee = *V

Heat gained by ice = heat lost by coffee
m*Lf + m*c (Tf-0) = ( *V)*c*(T-Tf)
m*Lf + m*c*Tf = ( *V)*c*T- ( *V)*c*Tf
m*Lf + m*c*Tf = ( *V)*c*T- ( *V)*c*Tf
m*c*Tf + ( *V)*c*Tf = ( *V)*c*T - m*Lf
(m+V)*c*Tf = ( *V)*c*T - m*Lf
Tf = [( *V)*c*T - m*Lf] / (m+V)*c

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.