Thermodynamics homework about 1st and 2nd Law

[alpyurtsever]

Homework Statement

A rectangular steel tank having an internal volume of 1 m3 contains air at 2.5MPa and 20°C. A relief valve is opened slightly allowing air to escape to the atmosphere. The valve is closed when the pressure in the tank reaches 350 kPa.
a) Calculate the amount of heat that must be added so as to keep the tank contents at 20°Cthroughout the process.
b) Calculate the final temperature if the process takes place adiabatically.

Homework Equations

I think 1st and 2nd Law of Thermodynamics must be used. I have tried to use them as it seem in my attachment.

The Attempt at a Solution

It is in my attachment.

Thank you :)

 

[nate808]

Hello,

Thank you for your post. I see that you have attempted to use the first and second laws of thermodynamics to solve this problem, which is a good start. However, I would like to offer some additional suggestions and clarifications.

First, let's define our system and surroundings. In this case, the system is the rectangular steel tank with the air inside, and the surroundings are the atmosphere. The heat added to the system will come from the surroundings, and the work done by the system will be done on the surroundings.

Next, let's consider the first law of thermodynamics. This law states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In this case, since the process is isothermal (the temperature remains constant at 20°C), the change in internal energy will be zero. This means that the heat added to the system will be equal to the work done by the system.

To calculate the work done by the system, we can use the ideal gas law, which relates the pressure, volume, and temperature of a gas. We can also use the definition of work, which is force multiplied by distance. In this case, the force is the pressure of the gas, and the distance is the change in volume of the gas. Since the tank is initially at a pressure of 2.5 MPa and a volume of 1 m^3, and the final pressure is 350 kPa, we can calculate the work done by the system as follows:

W = PΔV = (2.5 MPa)(1 m^3 - 0.001 m^3) = 2.499 MPa*m^3 = 2.499*10^6 J

This is the amount of heat that must be added to the system to keep the tank contents at 20°C throughout the process.

For part b, we can use the adiabatic process equation, which states that the product of pressure and volume raised to the ratio of specific heats (γ) is constant. In this case, the process is adiabatic, so there is no heat transfer (Q = 0). This means that the initial and final pressures and volumes are related as follows:

P1V1γ = P2V2γ

We know the initial pressure and volume, so we can solve for the final temperature as follows:

T2