Answer to Question #176236 in Physics for Kelly

Question

In a coffee shop, steam at 100 oC is passed into milk to heat it up and froth it. In this way 100 g milk is heated from 20 oC to 80 oC. Calculate the mass of steam that was condensed into the milk to bring this about. The specific heat capacity of water is 4.2 × 10^3 J kg–1 K–1, the specific heat capacity of milk is 4.0 × 103 J kg–1 K–1, and the specific latent heat of vaporisation of water is 2.2 × 10^6 J kg–1.

Answer 1

In order to heat $m=100g = 0.1kg$ of milk by $\Delta t = 80\degree C -20\degree C = 60\degree C$, the following amount of heat is required:

$$Q = c_mm\Delta t$$

where $c_m = 4\times 10^3\dfrac{J}{kg\cdot \degree C}$ is the  specific heat capacity of milk. If this amount of heat was taken from the vapor, the following mass should condense:

$$m_v =\dfrac{Q}{\lambda}$$

where $\lambda = 2.2\times 10^{6}J/kg$ is the  specific latent heat of vaporisation of water. Thus, obtain:

$$m_v = \dfrac{ c_mm\Delta t}{\lambda}\\ m_v = \dfrac{ 4\times 10^3\cdot 0.1\cdot 60}{2.2\times 10^6} \approx 10.9\times10^{-3}kg = 10.9g$$

Answer. 10.9 g.