The first step in solving this problem is to apply the first law of thermodynamics to the system. For this system, the first law can be expressed as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat transfer, and W is the work.
To calculate ΔU, we need to use the formula ΔU = m * Cv * (T2 - T1), where m represents the mass of air, Cv is the specific heat of air at constant volume, and T1 and T2 are, respectively, the initial and final temperatures of the air.
Given in the problem,
- mass of air (m) = 0.9 kg
- initial temperature (T1) = 300 K
- final temperature (T2) = 470 K
The specific heat of air at constant volume (Cv) is approximately 0.717 kJ/kg·K. So, we can calculate ΔU as:
ΔU = 0.9 kg * 0.717 kJ/kg·K * (470 K - 300 K) = 109.701 kJ
Next, the value of Q, which is the heat transfer from the air to its surroundings, is given as 20 kJ.
Now, we can use the first law of thermodynamics equation to calculate the work (W):
W = Q - ΔU = 20 kJ - 109.701 kJ = -89.701 kJ
The negative work indicates that work is done on the system.
Therefore, during the air compression, the change in internal energy is 109.701 kJ, and the work done on the system is 89.701 kJ.