Fuel 1
fuel
1
phase gas
phase: liquid
energy
transferred
out
fuel
2
fuel
2
phase, gas
phase: gps
engine OFF
engine ON
A certain type of ship has two tanks in its engine. Each tank contains a different
type of fuel. When the engine turns on, the same amount of energy is transferred
out of both fuels as shown in the diagram below. Why did fuel 1 change phase,
but fuel 2 stayed the same? Explain what happened to the molecules of both
fuels,

Part 1

Where we have that the phase temperature at which fuel 1 changes to liquid due to its low temperature after the energy transfer is reached, fuel 1 changes to liquid

Where we have that the temperature of fuel 2 is still above its gas to liquid phase transition temperature, the fuel in fuel 2 will remain gaseous

Part 2

The kinetic energy of the individual molecules in fuel 1 is less than the intermolecular forces holding the molecules of fuel 1 in the liquid state such that fuel 1 molecules undergoes phase transformation from gas to liquid

The kinetic energy of the molecules in fuel 2 is higher than the fuel 2 liquid state intermolecular forces fuel 2 does not undergo phase transformation and remain a gas

Explanation:

Part 1

Why fuel 1 change phase but fuel 2 stayed the same can be explained by the combination of the following physical phenomena

1) Specific heat capacity of the fuels

2) Phase transition temperature of the fuels

The energy transferred out, ΔQ, can be expressed as follows;

ΔQ = m·c·ΔT

Where;

m = The mass of the fuel

c = The specific heat capacity of the fuel

ΔT = The temperature change of the fuel

Therefore, the energy transferred out, for a given mass of fuel, is directly proportional to the specific heat capacity, and the temperature change

For a given amount of transferred energy, when the specific heat capacity is high, the temperature change will be low and vice versa

Taking the specific heat capacity of fuel 1, c₁ as lower than the specific heat capacity of fuel 2, c₂₂, we have;

For a given energy transferred out, when c₁ < c₂ then we have, ΔT₁ > ΔT₂

The temperature change of fuel 1 is more than the temperature change of fuel 2 and if both fuels where initially at the same temperature and have the same mass, the final temperature of fuel will be lower than the final temperature of fuel 2,

2) The phase transition temperature is the temperature at which a material changes phase from solid to liquid, or liquid to gas and vice versa, and it is dependent on the intermolecular holding the molecules of the substances together

Whereby the phase temperature at which fuel 1 changes to liquid due to its low temperature after the energy transfer is reached, while the temperature in fuel 2 is still above its gas to liquid phase transition temperature, the gaseous fuel in fuel 1 will be changed to liquid, while the fuel in fuel 2 will remain gaseous

Part 2

After the energy is transferred out, the kinetic energy of the individual molecules in fuel 1 becomes lower than the intermolecular forces holding the molecules of fuel 1 in the liquid state and the fuel 1 molecules transforms from gas to liquid

However, after the given amount of energy is transferred out, the kinetic energy of the molecules in fuel 2 are still higher than the intermolecular forces that exists between the molecules of fuel 2 when in the liquid state, and therefore, fuel 2 remains gaseous

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