To solve this problem, we need to use 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. In this case, the work is done on the system, so it is negative. The equation is:

ΔU = Q - W

We know that the change in internal energy (ΔU) of an ideal gas is given by:

ΔU = m * c_v * (T2 - T1)

where m is the mass of the gas, c_v is the specific heat at constant volume, T1 is the initial temperature, and T2 is the final temperature.

First, we need to find the mass of the nitrogen. We can use the ideal gas law, which states that P * V = m * R * T, where P is the pressure, V is the volume, R is the gas constant, and T is the temperature. Solving for m gives:

m = P * V / (R * T)

Substituting the given values (converting temperatures to Kelvin and pressures to kPa), we get:

m = 150 kPa * 0.1 m^3 / (0.2968 kJ/(kgK) * (25°C + 273.15)) = 1.81 kg

Next, we substitute the values into the equation for ΔU:

ΔU = 1.81 kg * 0.745 kJ/(kgK) * ((150°C + 273.15) - (25°C + 273.15)) = 136.6 kJ

Finally, we substitute the values for ΔU and W into the first law of thermodynamics to find Q:

Q = ΔU + W = 136.6 kJ + (-20 kJ) = 116.6 kJ

So, the heat transferred from the nitrogen during the compression process is 116.6 kJ. However, since heat is transferred from the nitrogen, the heat transfer is negative, so Q = -116.6 kJ. This is not one of the options given in the question, so there may be a mistake in the problem or in the provided options.

Question

To solve this problem, we need to use 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. In this case, the work is done on the system, so it is negative. The equation is:

ΔU = Q - W

We know that the change in internal energy (ΔU) of an ideal gas is given by:

ΔU = m * c_v * (T2 - T1)

where m is the mass of the gas, c_v is the specific heat at constant volume, T1 is the initial temperature, and T2 is the final temperature.

First, we need to find the mass of the nitrogen. We can use the ideal gas law, which states that P * V = m * R * T, where P is the pressure, V is the volume, R is the gas constant, and T is the temperature. Solving for m gives:

m = P * V / (R * T)

Substituting the given values (converting temperatures to Kelvin and pressures to kPa), we get:

m = 150 kPa * 0.1 m^3 / (0.2968 kJ/(kgK) * (25°C + 273.15)) = 1.81 kg

Next, we substitute the values into the equation for ΔU:

ΔU = 1.81 kg * 0.745 kJ/(kgK) * ((150°C + 273.15) - (25°C + 273.15)) = 136.6 kJ

Finally, we substitute the values for ΔU and W into the first law of thermodynamics to find Q:

Q = ΔU + W = 136.6 kJ + (-20 kJ) = 116.6 kJ

So, the heat transferred from the nitrogen during the compression process is 116.6 kJ. However, since heat is transferred from the nitrogen, the heat transfer is negative, so Q = -116.6 kJ. This is not one of the options given in the question, so there may be a mistake in the problem or in the provided options.

Knowee AI · Accepted Answer