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Question 8

Espresso is a coffee beverage made by forcing steam through finely ground coffee beans. Modern espresso makers generate steam at very high pressures and temperatures, but in this problem we'll consider a low-tech espresso machine that only generates steam at 100 °C and atomospheric pressure--not much good for making your favorite coffee beverage.

The amount of heat 'Q' needed to turn a mass 'm' of room temperature (T1) water into steam at 100 °C (T2) can be found
using the specific heat 'c' of water and the heat of vaporization 'Hv' of water at 1 atmosphere of pressure.

 

Part A:
Suppose that a commercial espresso machine in a coffee shop turns

1.50 kg of water at 22.0 °C into steam at 100 °C. If c = 4187 J/(Kg °C) and Hv = 2258 kJ/Kg, how much heat 'Q' is absorbed by the water from the heating resistor inside the machine?

Assume that this is a closed and isolated system. Express your answer in joules to three significant figures.

 

Part B: 

In an electric espresso machine, a resistor produces the heat to boil the water. If the resistor has a power output P of 1200 W, 

approximately how much time 't' would it take to completely change the 1.5 kg of water into steam if the initial water temperature is 22 °C?

Give the amount of time required rounded to the nearest minute.

 

Part C:
Many people use a natural gas called propane (C3H8) to cook with and to heat their homes. The molar mass of propane is 44.1 g/mol. When one mole of propane burns, it releases 2219 kJ of energy. If the espresso machine uses propane gas instead of electricity to boil the 1.50 kg of water at an initial temperature of 22.0 °C, what mass of propane gas is needed to change all of the water to steam?.

Assume that the espresso machine is still a closed, isolated system and that all of the heat released from burning is used to heat the water.

Express the answer in grams to three significant figures.