# First law of thermodynamics applied to a submarine

• Carbon884
In summary, the first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. In the given scenario, a submarine with a volume of 1000m^3 and air temperature and pressure of 15°C and 0.1MPa respectively, experiences a heat flow of 60 MJ/h and dissipative work of 21 kW. Using the first law, the average temperature of the air after one hour of diving can be calculated. However, the calculation may be incorrect as the specific heat capacity and internal energy values used do not match. It is also mentioned that the pressure may increase with temperature in this constant volume process.
Carbon884
First law of thermodynamics

Hallo,

i hope someone can help me with the following question:

A submarine contaiins 1000m^3 of air and has a temperature and pressure of 15°C and 0.1MPa respectively. Due to the cold seawater a heatflow of 60 MJ/h occurs. The machines on the otherhand add disspiative Workof 21 kW to the system. The specific heat capacity of air is c(p,air) = 1.005 kJ/Kg*K.

what average Temperature will the air have after one hour of diving?

V=constant=1000m^3
P=constant?
T1=288.15K => T2=?

Firstly i found the density and mass of the gas:

R(air)= 286.9 J/K*Kg => density= P/T*R(air)=1.209 Kg/m^3 => m= V*density= 1209.63 Kg

Secondly i found the total Energy:

Q/h=Wdiss - Q/h = 15600 KJ/h

Then i used the first law:

dW=0 because V=constant

dQ=dU

Q=mcp(T2-T1)= m(R(air)-cv)*(T2-T1)= 288.19K ... which can't possibly be right because that is essentially my T1 temerature. So what did I do wrong?

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Carbon884 said:
Q=mcp(T2-T1)= m(R(air)-cv)*(T2-T1)= 288.19K ... which can't possibly be right because that is essentially my T1 temerature. So what did I do wrong?
I am not sure I follow what you have done here. Since it is a constant volume process you have to find Cv. You are given Cp. So what is Cv for the air?

AM

R(air)= cp-cv => cv=R(air)+cp...i accidentally wrote a minus sign but i meant plus -.-.

What I can't really imagine though is what happens to the pressure during this process?

Carbon884 said:
R(air)= cp-cv => cv=R(air)+cp...i accidentally wrote a minus sign but i meant plus -.-.
I think you meant: Cv = Cp-R.

What I can't really imagine though is what happens to the pressure during this process?
If the submarine is air-tight and rigid, the volume is constant and the quantity of gas does not change. Since heat flow is into the submarine, temperature goes up. Apply the ideal gas law:

PV = nRT

If V and n are constant, what must happen to P if T increases?

AM

*nods* so the pressure will increase with temperature.

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## 1. How does the first law of thermodynamics apply to a submarine?

The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another. In a submarine, this law applies to the conversion of energy from the submarine's power source (usually a nuclear reactor or diesel engine) into mechanical energy to power the propellers and move the submarine through water.

## 2. How is energy conserved in a submarine?

The first law of thermodynamics also applies to the conservation of energy in a submarine. This means that the total amount of energy in the system remains constant, even as it is converted from one form to another. In a submarine, this conservation of energy is important for maintaining the balance of power and propulsion systems, as well as the overall operation of the vessel.

## 3. What role does heat play in the first law of thermodynamics on a submarine?

Heat is a form of energy and is an important part of the first law of thermodynamics on a submarine. In order for the submarine's power source to convert fuel into mechanical energy, heat is needed to drive the reaction. Heat is also produced as a byproduct of the power generation process and must be managed and controlled to maintain the submarine's temperature and prevent damage to equipment.

## 4. How does the first law of thermodynamics affect the efficiency of a submarine?

The first law of thermodynamics dictates that energy cannot be 100% converted from one form to another without any loss. In a submarine, this means that there will always be some energy lost in the conversion process, resulting in decreased efficiency. Submarine designers and engineers must take this into account when designing and optimizing the power and propulsion systems to ensure the most efficient operation possible.

## 5. What are some real-world examples of the first law of thermodynamics applied to submarines?

One example of the first law of thermodynamics in action on a submarine is the use of a nuclear reactor as a power source. The nuclear reaction produces heat, which is then converted into mechanical energy to power the submarine. Another example is the use of heat exchangers to transfer heat from the reactor to other systems on the submarine, such as the propulsion system or onboard equipment, to utilize as much energy as possible.

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