Question

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.

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Question: Espresso is a coffee beverage made by forcing steam through finely ground coffee beans. Modern es...

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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 Celcius 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 ( T_1) water into steam at 100 Celcius. ( T_2) can be found using the specific heat, c, of water and the heat of vaporization, H_v, of water at 1 atmosphere of pressure.

Suppose that a commercial espresso machine in a coffee shop turns 1.50 kg of water at 22.0 Celcius into steam at 100 Celcius. If c = 4187 J/(kg * C) and H_v=2,258 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.



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 Celcius?

Part C
Many people use a natural gas called propane (C_3H_8) 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 Celcius, what mass, m_propane, 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.

Answer 1

Part A

The amount of heat Q needed to turn a mass, m = 1.50 Kg, of room temperature ( T₁= 22.0 ºC) water into steam at . ( T₂= 100.0 ºC), is given by:

Substituting in the previous equation the given data of mass, calorific capacity, heat of vaporization and temperatures for water, it is necessary that the amount of heat Q will be:

Data:

c = 4187 J/(kg * C) and H_v=2,258 kJ/kg

Then, the amount of heat Q needed to turn a the mass of 1.50 kg of water from 22ºC to 100ºC will be:

Part B

The power P is given by:

Where:
W: is the work required to transfer heat to water from 22 ºC to 100 ºC, determined in part A, that is, W = Q = 493266 J
t: it is the time required for that heating

Data:

P = 1200 W = 1200 J/s

By clearing time t from the power equation and substituting the data, we have:

Since 1 min = 60 s

Then, the time, t, would it take to completely change the 1.5 kg of water into steam if the initial water temperature is 22 Celcius, will be:

Part C

according to the problem data:

1 mole of C₃H₈ It represents 44.1 g and

1 mole of C₃H₈ produces an energy of 2219 kJ

From the above it is concluded that:

44.1 g of C₃H₈ produces an energy of 2219 kJ

Then the mass m of propane required to heat the mass 1.5 kg of water from 22 ºC to 100 ºC, whose energy is 493266 J, will be:

then m (g) will be: