in an espresso machine, steam at 100 degrees celcius is bubbled into milk to heat it. the specific heat capacity of milk is 4.0 x 10^3 J/kg Kcalculate the energy required to heat 150g of milk from room temperature of 25 degrees celcius to 80 degrees celciuscalculate the mass of steam condensed in the process

To solve this problem, we need to use the formula for heat transfer:

Q = mcΔT

where: Q = heat energy (Joules, J) m = mass (kilograms, kg) c = specific heat capacity (Joules per kilogram per degree Celsius, J/kg°C) ΔT = change in temperature (degrees Celsius, °C)

First, we need to convert the mass of the milk from grams to kilograms, because the specific heat capacity is given in J/kg°C.

150g = 0.15kg

Next, we calculate the change in temperature:

ΔT = T_final - T_initial = 80°C - 25°C = 55°C

Now we can calculate the energy required to heat the milk:

Q = mcΔT = 0.15kg * 4.0 x 10^3 J/kg°C * 55°C = 33000 J

The second part of the question asks for the mass of steam condensed in the process. To find this, we need to know the heat of vaporization of water, which is approximately 2260 kJ/kg.

The energy from the condensed steam is equal to the energy required to heat the milk, so we can set up the equation:

Q = mL

where: Q = heat energy (Joules, J) m = mass (kilograms, kg) L = heat of vaporization (Joules per kilogram, J/kg)

Rearranging for m gives us:

m = Q / L = 33000 J / 2260 x 10^3 J/kg = 0.0146 kg

So, the mass of steam condensed in the process is approximately 0.0146 kg.