i) The work done during compression can be calculated using the formula for work done on a gas during polytropic compression, which is:

W = (P2*V2 - P1*V1) / (1-n)

where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and n is the polytropic index. In this case, n = 1.2.

First, we need to find the final volume V2. We know that P1*V1^n = P2*V2^n, so we can rearrange this to find V2 = (P1/P2)^(1/n) * V1 = (100/1500)^(1/1.2) * 0.15 = 0.042 m^3.

Then we can substitute these values into the formula for work:

W = (1500*0.042 - 100*0.15) / (1-1.2) = -105 kJ

The negative sign indicates that the work is done on the gas.

ii) The mass of the gas can be found using the ideal gas law, PV = mRT, where m is the mass, R is the specific gas constant, and T is the temperature in Kelvin. Rearranging for m gives m = PV / RT.

First, we need to convert the temperature from Celsius to Kelvin: T = 20 + 273.15 = 293.15 K.

Then we can substitute the known values into the formula:

m = 100*0.15 / (287*293.15) = 0.0018 kg

iii) The change in internal energy can be calculated using the formula ΔU = m*Cv*ΔT, where ΔU is the change in internal energy, Cv is the specific heat capacity at constant volume, and ΔT is the change in temperature.

First, we need to find the final temperature T2. We know that T1*V1^(n-1) = T2*V2^(n-1), so we can rearrange this to find T2 = T1 * (V1/V2)^(n-1) = 293.15 * (0.15/0.042)^(1.2-1) = 1085 K.

Then we can calculate the change in temperature: ΔT = T2 - T1 = 1085 - 293.15 = 791.85 K.

Substituting these values into the formula gives:

ΔU = 0.0018*7180*791.85 = 10.2 kJ

iv) The heat transferred during compression can be calculated using the first law of thermodynamics, which 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. Rearranging for Q (the heat transferred) gives Q = ΔU + W.

Substituting the known values gives:

Q = 10.2 - (-105) = 115.2 kJ

The positive sign indicates that heat is supplied to the gas.

Question

i) The work done during compression can be calculated using the formula for work done on a gas during polytropic compression, which is:

W = (P2*V2 - P1*V1) / (1-n)

where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and n is the polytropic index. In this case, n = 1.2.

First, we need to find the final volume V2. We know that P1*V1^n = P2*V2^n, so we can rearrange this to find V2 = (P1/P2)^(1/n) * V1 = (100/1500)^(1/1.2) * 0.15 = 0.042 m^3.

Then we can substitute these values into the formula for work:

W = (1500*0.042 - 100*0.15) / (1-1.2) = -105 kJ

The negative sign indicates that the work is done on the gas.

ii) The mass of the gas can be found using the ideal gas law, PV = mRT, where m is the mass, R is the specific gas constant, and T is the temperature in Kelvin. Rearranging for m gives m = PV / RT.

First, we need to convert the temperature from Celsius to Kelvin: T = 20 + 273.15 = 293.15 K.

Then we can substitute the known values into the formula:

m = 100*0.15 / (287*293.15) = 0.0018 kg

iii) The change in internal energy can be calculated using the formula ΔU = m*Cv*ΔT, where ΔU is the change in internal energy, Cv is the specific heat capacity at constant volume, and ΔT is the change in temperature.

First, we need to find the final temperature T2. We know that T1*V1^(n-1) = T2*V2^(n-1), so we can rearrange this to find T2 = T1 * (V1/V2)^(n-1) = 293.15 * (0.15/0.042)^(1.2-1) = 1085 K.

Then we can calculate the change in temperature: ΔT = T2 - T1 = 1085 - 293.15 = 791.85 K.

Substituting these values into the formula gives:

ΔU = 0.0018*7180*791.85 = 10.2 kJ

iv) The heat transferred during compression can be calculated using the first law of thermodynamics, which 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. Rearranging for Q (the heat transferred) gives Q = ΔU + W.

Substituting the known values gives:

Q = 10.2 - (-105) = 115.2 kJ

The positive sign indicates that heat is supplied to the gas.

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