thermodynamics questions please answer all 4 of them

Question

1) A constant volume process occurs in a closed container that has a volume of 4 m ³. Heat is added to the container such that the absolute pressure increases 120 kPa to 207 kPa. What is the work done by gas on the container in kJ?

2) A constant pressure process occurs in a piston cylinder assembly that initially has an absolute pressure of 237 kPa. Heat is added to the assembly such that the volume increases from 1.4 m ³ to 3 m ³ . What is the work done by gas on the container in kJ?

3) A polytropic process ( n = 1.4) occurs in a piston cylinder assembly that initially has an absolute pressure of 2,134 kPa. The gas does work on the piston such that the volume increases from 0.07 m ³ to 0.74 m ³ . What is the work done by the gas on the piston in kJ?

4) Which of the following statements are true?  (Choose all that apply)

1. Work into a system is considered negative
2. Heat out of a system is considered positive
3. Work out of a system is considered positive
4. Heat into a system is considered negative.
5. Heat into a system is considered positive
6. Work into a system is considered positive

Answer 1

Let's address each of these thermodynamics problems one by one:

1. Constant Volume Process

In a constant volume process, the work done is zero because work ( W ) is defined as the product of pressure change and volume change (W = P ΔV ). Since the volume does not change (ΔV = 0 ), no work is done, regardless of the pressure change. Thus, the work done by gas on the container is 0 kJ.

2. Constant Pressure Process

For a constant pressure process, the work done by the gas can be calculated using the formula ( W = P ΔV). Here, ( P) is constant at 237 kPa and the volume change (ΔV ) is from 1.4 m³ to 3 m³.

W = P ΔV = 237 {kPa} ×(3 - 1.4) {m³} =379 kJ

3. Polytropic Process

In a polytropic process, the work done is given by the formula ( W = (P₁ V₁ - P₂ V₂)/(n-1). Since n = 1.4 , P₁ = 2134 {kPa} , V₁ = 0.07 {m³}, and V₂ = 0.74 {m³}, we first need to find P₂ using the polytropic relation:

P₁ V₁ⁿ = P₂ V₂ⁿ

P₂ = P₁ ( V₁/V₂)ⁿ

After finding P₂=78.6kPa, we can then calculate W =228 kJ.

4. Statements about Work and Heat

1. Work into a system is considered negative: True. When work is done on the system, it's considered as input, hence negative.
2. Heat out of a system is considered positive: False. Heat out of a system is considered negative (loss of energy from the system).
3. Work out of a system is considered positive: True. When the system does work on the surroundings, it's considered as output, hence positive.
4. Heat into a system is considered negative: False. Heat into a system is considered positive (gain of energy to the system).
5. Heat into a system is considered positive: True.
6. Work into a system is considered positive: False. As stated earlier, work into a system is negative.